Although @aslum's and @J. A. Streich's answers talk about not being able to take Long Rests as frequently as the Wizard would like, no-one has mentioned that this is explicitly stated in the PHB page 186 under the definition of a long rest:

A character can’t benefit from more than one long rest
in a 24-hour period, and a character must have at least
1 hit point at the start of the rest to gain its benefits.

So the party are not just waiting another 8 hours per Long Rest. They are waiting 24 hours.

The Party

You have a balanced party. What they want makes sense.

• The wizard is pretty cautious... because they are a wizard and are squishy.


• The druid's player likes doing things that would be in character even if they aren't completely optimal, and likes the feeling of danger... because they are a cool Druid, and there is depth there. Right.


• We also have a monk who's frustrated by doing less damage than the other PCs (particularly the wizard). Yep. But monk's get really neat abilities later in the game, and it makes sense that the player would feel a little underwhelming at lower levels.

Long Rests

So days with multiple encounters and short rests are preferable to me, the druid, and the monk, and is also the way the game is ''supposed'' to be, if that means anything. One battle then a long rest is preferable to the wizard (for obvious reasons, I guess), and the rogue doesn't mind.

Great. Actions have consequences. Party wakes up 7 AM. Eats breakfast. Runs into some Orcs. Fights 3 rounds of combat (3 rounds * 6 seconds is 18 seconds later) and then wants to go back to sleep at 8 AM. So, you're the DM, what do you do?

Actions have consequences. Options you can use:

• 
  Monsters have friends. Ambush the party two hours later, when the orc party searches for the missing patrol the party just killed. This ruins the long rest. You don't have to always interrupt the sleep, but keep in mind that sleeping near the enemy at 10 AM is a bad idea in real life too. Also, a Nightmare Hag would love feasting on a party that only stays awake for an hour at a time.


• 
  People have circadian rhythms. You simply can't fall asleep, the bright sun in your eyes and heavy breakfast YOU JUST ATE are preventing you from getting any shut eye. After laying there restless for an hour or so, what would you like to do? (and the rules support this (thanks Black Spike for finding PHB page 186):
  
  

  
  

  A character can’t benefit from more than one long rest in a 24-hour period, and a character must have at least 1 hit point at the start of the rest to gain its benefits.

  
  

  
  


• 
  Things don't stop because the players sleep. While the party is asleep, the BBEG conquers more land, takes more prisoners, and magical darkness spreads to the edges of another town. The big bad kidnaps one adventurer's relative, and kills five town guards. It might have been prevented, but you were asleep. The king is angry, he hoped people with your skill wouldn't be caught laying down on the job.


• 
  Things happen at specific times "You can sleep, but you have to meet with Balalabad in an hour, and you are an hour and a half travel time from them at normal walking speed. Guess you don't want the reward for the gem you risked your life to steal from the giant for them."


• 
  Let them split the party You have two players who want sleep, two who want to keep going. The monk and druid decide (maybe with the helpful DM comment, "just because they are sleeping doesn't mean you have to.") to keep going while the wizard and rogue snore. I don't often suggest splitting the party, but I don't think it would split the party. I think the rogue will likely decide the rest isn't worth not getting the XP and the possibility the monk and druid might not share their findings. Now, will the squishy wizard still think sleeping alone in the middle of dungeon full of hostile monsters is the best course of actions?

I'm frustrated that in a recent session, what was supposed to be
multiple encounters [became] one minor battle and a long rest.

Why won't the encounters just happen next session? What held off the other encounters? Why did one encounter and sleep take a whole session? I mean sleep, when you let them actually sleep is, "Oh, you want to sleep? Alright... You go to sleep." (give time for someone to say if/who is on watch. If no one, then you'll have real fun.) "You are woken up an hour later to the strong hands (or tentacles) wrapping around your arms..."

Sooth Your Doubts

Is this a sign that the players are too different for us to happily play together, or just that I'm a bad DM?

Neither. Long rests are often points of contention between players and DMs, until or unless expectations are set. I think it is a common struggle with caution and risk. Some of it can be mitigated in game as above. Seeing that things happen in the world while the party argues or sleeps makes the game world feel more real. That characters exist in a larger world, not that the world exists for the players to live in. It isn't a video game with a pause button.

Some of it might have to come from a session 0 like talk, where you ask them what their expectations are, tell them what yours are. In it assure your wizard player that, "I'm not here to kill your character. I'm here to make your character shine by giving them opportunities to pull through when the chips are down. To do that, there will be some risk of character death, but without the risk the reward isn't as meaningful. No one likes the story about the wizard who went to sleep. They like the story about the wizard who used their last spell slot to cast enlarge on the party's monk (who only had one hit point left) and the monk super puched a dragon in the face as the final blow in an epic battle. Trust me not to be gunning your characters down, and take a little more risk – it will be worth it."

There's a few things you can do to help solve this.

Not everywhere is safe to take a long rest

If you try to take a long rest somewhere unsafe there's a good chance your rest will get interrupted, and then you'll have to start again. Dropping a DM hint (such as "from the tracks through here it's obvious this area sees a lot of traffic") that an area might not be safe, especially early on, can help encourage the party progress further.

A long rest is 8 hours

Trying to sleep and rest when you're not tired is kind of hard. Worse, people have natural rhythms to their sleep cycles, and trying to change it is hard. If they take an 8 hour rest in the middle of the afternoon, they're still going to be getting sleepy in the evening, and if they do keep on with their aberrant rest/wake cycle you might want to apply some variant of the fatigue rules.

Some monsters are more effective during the night / NPCs might be sleeping

Finally, if they're taking rests at weird times, they're going to end up running into monsters during the night, and some monsters could have an advantage whether from being nocturnal or the party not having Darkvision. It might also make meeting friendly NPCs harder!

Throw them into a scenario where they can't rest

For example, they are hired to acquire an artefact. The artefact is in a city - so they travel there.

Once there, they discover that the artefact is the prize for a tournament in a coliseum. They enter, they have to try to win (or, at least, come up with a plan to get the artefact from whoever does win - trade, theft, bribery, whatever)

Now, this means that the combat times are fixed. So, Mr Wizard - you have 3 or 4 fights to win, with increasingly difficulty. But, you only get a 2-hour break between them, so no chance for a long rest. A short rest will be fine though.

You can throw in side-quests that let them gain information about their upcoming opponents (or chances to sabotage them) - but, if they take too long on these then they might have to forgo the Short Rest.

The Wizard is then forced to either conserve powerful spells for the later rounds - meaning he does less damage in earlier rounds - or spend them in the early rounds and eek out his remaining resources as the day goes on. The Monk gets to shine as a "sustained" combatant, managing about the same in every round. The Druid gets multiple fights, and at some of these will be harder by dint of the Wizard conserving (or running out of) spells.

If you do do this though, try to set up a couple of "clever" things that the wizard can do - environmental hazards or enemies that will interact with low level spells / cantrips, to encourage them to use those in place of burning their big-guns. The idea is not to make the wizard feel "weak" or "useless", but to make them think about how best to use all their spells. Make them feel clever about it - Intelligence and Wisdom are their main stats after all

And of course, they'll all know when the "final round" is, and can go all-out, safe in the knowledge that they get a long rest before any more combat can happen.

To summarize the problem:

• Player One wants an infinite sequence of pitched maximal-force battles followed by long rests


• Player Two probably wants, but cannot articulate, a sequence of days with more battles punctuated by short rests, and comparatively fewer long rests


• Player Three has no expressed mechanical preference, but in a desire for "more danger" probably leans toward Player Two

What you can't do:

Assuming that assessment on your part is correct, Players One and Two are in direct opposition and their desires cannot be mutually satisfied at the same time. You cannot both have and not-have all of those long rests.

What you can do:

1. But you can satisfy these desires sequentially, one at a time. If my assessment is correct and players two and three are in agreement, you can write adventure arcs catering to them roughly 2/3 of the time, and to player one roughly 1/3 of the time.




2. Alternately, as a frame challenge, you can decide which one (or more) of them are "correct" and cater only (or mostly) to them. I am going to go out on a limb and suggest that in this case, Player One is, intentionally or not, deviating from the spirit of the rules, trying to avoid the issue of strategically managing spells over the course of a day. He effectively wants to buff himself to constantly maximum strength with all those long rests, and probably should not be indulged very often.

How To Do It:

Either of those solutions, though, involves shutting down Player One's long rest strategy some or all of the time.

1. You can do this on a meta-level, out of character, either by explaining to that player that he's having harmful effects on the other players. You can, frankly, just disallow it. You're the GM and other players get votes about party activities. I find that unsatisfying, though.



2. 
   

   Time Pressure! There are infinite opportunities to create time pressure in a game that simply preclude Player One from spending each adventuring day as 15 minutes of furious action, followed by 23 hours and 45 minutes of rest and I've probably used them all:

   
   
   

   • The Deadline: "If we don't make it to the top of the Ziggur-mid of Doom by Grunsday the 27th to shut down their foul ritual, they will succeed in summoning Zuul!"

   
   

   • The Chase I: Whether they're chasing someone over the course of a single day, or an extended period of weeks, nothing adds time pressure like a chase.

   
   

   • The Chase II: As above, but now the party is being chased (probably by a force, not an individual) and need to make it to safety.

   
   

   • The Race: An unspecified deadline, where all the group knows is that some other active force is pursuing the same goal and they need to get there first.

   
   

I find time pressure (and related strategies, like environments that are hostile to long rests) more satisfying and effective because rather than just dictating something out of game, or using indirect hints like wandering monsters, the time pressure is baked into the adventure design. It is something Player One's character must grapple with, directly and can even be an occasion for role play: Is he really so timid that he'll allow the Virgin Prince to be sacrificed at the top of the Ziggur-mid?

Actually, I suggest changing things a bit to reflect an old story called Tuckers kobolds back from the days of 1st or 2nd.

The party was in some kind of mine and each day they would try to access deeper and deeper levels. However on an early level before the elavator for the mine, they had to bypass the kobolds, both ways. They were expertly run and frequently used hit and run tactics.

The moral I am trying to get at here is that dont let the first combat be the focus. This experienced group never got anything of value or XP from defeating these low level creatures, and if they stopped every time they interacted, they would never be able to reach their goal deeper inside the mine.

If the party realizes that the wizards reliance on their strongest spells in situations is preventing them from moving on, then hopefully the party will address the issue for you. This should hopefully push the party past the 5 minute adventuring day and allow the monk to feel more useful and take advantage of the short rests. Multiple combats also allows the druid to do more and sure an encounter may be easy, but the second and third become more difficult as resources have been exhausted.

It's hard to blame the wizard's player for using this (annoying) strategy, when it's the optimal strategy. If there are no consequences for delays, then taking on everything at fresh full power is optimal.

So you need to introduce consequences and trade-offs. Sometimes the players get to choose whether to delay. Sometimes they can't delay (trapped behind enemy lines, constant patrols, can't rest until you're back), sometimes they must delay (after 1-2 days, you get so exhausted you just have to rest). But in many cases the players should be asking themselves "can we go on? What if we don't?"

Since your players have "learned" that they can rest at will with no consequences, if you suddenly put them in a situation where they absolutely have to keep going on, they'll be in deep trouble. The wizard will be out of spells and they'll take a hammering. You have to re-educate them.

So it could be better to start by doing a voluntary "extra effort". Say they come to a dungeon on day one, and murder the first room and then go back to rest. Next day they come to the dungeon and it's empty. Everyone's gone, and they took the treasure with them. But there's tracks they can follow. When they do, they run into some more enemies, but these turn out to be the rear guard, the main group with the treasure is up ahead. If the group rests now, the main group will be so far ahead that the PCs won't catch up. They have a choice: press on and have another fight today, or give up on the treasure. Now, resting isn't the obvious optimal strategy anymore.

A second thing to experiment with is random encounters. Random encounters have a couple of functions:

• Create the feeling the whole world doesn't revolve around the PCs and
  their current plot.


• Show off the area the PCs are in by running into some signature monsters. A rock-throwing giant in the mountains, a plant monster
  that tries to drag you underwater in the swamp, the annoying monkey
  people in the forest that attack you from out of the trees.


• Make it unpredictable how many encounters there will be in a day.

Now you don't actually have to make them all random, as long as they seem to be so. Put on your poker face, roll dice and go "oh-oh" at the players. Don't make the random encounters more powerful than the main story ones though. A not too hard encounter that the wizard didn't count on but he's out of his best spells because he was sooo sure there'd only be one fight that day.

I think Novak makes a good point that you should also take the wizard's preferences into account. Don't enforce 4 encounters per day because it's orthodox. Some days it'll really just be one (hard) fight. Some days it'll be a couple of easier fights. Sometimes it'll be a longer than expected series of fights, and by the end everyone is running on fumes. Sometimes the PCs have the advantage and can pick their battles. Sometimes they're under pressure and stuff is just happening to them. Sometimes it's up to them to decide whether they think they can push on for gold and glory. Sometimes they're just trying really hard to set up a hidden camp because they're in wild lands and need some rest to recover.

A thing to consider with the wizard is that although canonically part of the "fun" of playing a wizard is challenging resource management, that might not be what your player signed up for. Maybe he mostly just likes being at the height of power. So he's not playing the wizard the way he's "supposed" to in a "model" game. Don't be too harsh in telling him he's wrong though. The point of RPGs is to all have fun, not to impress the internet by how correctly you're playing.

Some more ideas about different styles of time pressure:

1. It can take the monsters an hour to notice the patrol hasn't come
   back. If the PCs delay, the monsters go on alert. They may bring in
   reinforcements so encounters are going to be harder; they're not all
   waiting in separate rooms anymore. Taking on the whole dungeon at
   once can be tricky.


2. As (1), but the monsters go looking for the
   PCs after an hour.


3. As (1), but the monsters evacuate and take
   their treasure with them.


4. As (1), but the monsters start the
   ritual early and half the prisoners are already sacrificed by the
   time they burst into the boss room.


5. A really big bad thing is
   slowly getting closer. It's too powerful to face even with the PCs
   at full strength. Only if you find the weapon that can hurt it or
   the ritual that can block it's power do you stand a chance. If you
   take too long to get there, it's game over. Campaign lost. You have
   a couple of slack days, but every delay has to be carefully
   considered.


6. A PC has a nasty disease and gets sicker every day
   until a cure is found.


7. Every time you destroy the ghost in the
   first room, it returns 1d4 days later until you find out how to lay
   it to rest forever.


8. In a week, the rival adventuring group will
   also get to the dungeon and you'll have to fight for it, unless of
   course you're already done by then.


9. The PCs need the MacGuffin to
   impress the king, but another group of adventurers is elsewhere also
   looking for one, and might get back sooner if the PCs take their
   time.

I think the most interesting from a time/resource management standpoint are the ones where there are legitimately too many things to do in one day, but there's time pressure so you constantly have to ask "can we do one more today?".

From Matthew Colville's excellent "Running the Game" vlog series, the "Random Encounters" episode includes some great insights about players or parties that are prone to take frequent rests to heal or recover spells.

The gist: the possibility that a long rest will result in an encounter with a nasty beast (often nastier than those they would have encountered in the normal course of the adventure) is a great incentive for players to crack on.