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In the first book of the Harry Potter series, Hagrid says that Quirrell met vampires in the Black Forest and it changed him. However, the Black Forest is in Germany, and it is said that Voldemort was hiding in the forests of Albania, waiting for his followers.

Was Quirrell actually in Germany or did he use this story as a cover? Dumbledore clearly knew that Quirrell was in Albania because he researched it later. I have doubts, however, because in several places it says that he "met with vampires in the Black Forest, in Albania".

Is there a forest named as such in Albania? I really couldn't find anything.

Quirrell probably visited both Germany and Albania on his travels.

The only time we hear about Quirrell's time in the Black Forest was from Hagrid, who in turn is recounting rumours he's heard about his travels.

"He was fine while he was studyin’ outta books but then he took a year off ter get some first-hand experience...They say he met vampires in the Black Forest, and there was a nasty bit o’ trouble with a hag - never been the same since."
_{(Philosopher's Stone, Chapter 5, Diagon Alley).}

It seems that a palpable change in Quirrell's demeanour was noticed when he came back from his trip to Europe. Whether he actually went to Germany or not is unclear. However, we do know that he travelled abroad in a "Grand Tour" before he started teaching.

Harry’s first Defence Against the Dark Arts teacher is a clever young wizard who took a ‘Grand Tour’ around the world before taking up his teaching post at Hogwarts.
_{("Professor Quirrell", Pottermore).}

This may well be the sort of tour that Doge and Dumbledore intended to go on together. Such tours were necessarily international in nature and involved visiting multiple foreign wizarding cultures.

When Albus and I left Hogwarts we intended to take the then-traditional tour of the world together, visiting and observing foreign wizards, before pursuing our separate careers.
_{(Deathly Hallows, Chapter 2, In Memoriam).}

Quirrell himself also says that he met Voldemort when he "travelled around the world" (thanks to Alex for the quote). He was going on a lengthy excursion across multiple countries rather than simply visiting one country.

“He is with me wherever I go,” said Quirrell quietly. “I met him when I travelled around the world. A foolish young man I was then, full of ridiculous ideas about good and evil. Lord Voldemort showed me how wrong I was."
_{(Philosopher's Stone, Chapter 17, The Man With Two Faces).}

It would be absolutely consistent, therefore, to say that Quirrell visited both Germany and Albania. He probably visited a few other countries as well.

Quirrell's intention in travelling was to locate Voldemort.

Quirrell set out deliberately to find whatever remained of the Dark wizard, partly out of curiosity, partly out of that unacknowledged desire for importance.
_{("Professor Quirrell", Pottermore).}

It would also make sense that Quirrell visited a few places when trying to find Voldemort. Depending on how much he knew, he could have just been travelling almost at random. We know that Dumbledore had unspecified "sources" telling him that Voldemort was in Albania. Quirrell may not have had that information. It seems probable to me that Quirrell travelled across Europe looking for Voldemort, taking in the Black Forest and Albania on the way. Rumours of at least part of the trip made it back to Britain, rumours which Quirrell and Voldemort would have permitted to spread since they made the trip sound innocuous.