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Prague: What are the most popular areas in Prague?
Unless you insist on staying in the city center I would recommend looking for spots in Prague 6. It is much quieter and since Prague is really small, you can be in the center in 15 minutes by tram.
Prague: Visiting Prague, what other city to visit for a few days by train or air?
Budapest is a very cool city, which has a similar vibe as Prague. Vienna, on the other hand, is quite a typical "dry" touristy city. If you haven't been to Berlin yet, it would...