Unique, Modern, Fun, Old, Haunting....GO!
Budapest is definitely the city to be right now. It has everything you want in a European city, and at the moment, it probably has the least amount of tourists for a city of this size (there are still tourists, but no where near as bad as most major Euro cities). The buildings are all gorgeous, there are a ton of castles/religious buildings, and everything about this place rules. This place a communist horror show 25 years ago....but the city flourishes with modernization. It's awesome.
Insider Tip:Ruin pubs. They are what it sounds like. Abandoned buildings and lots turned into pubs (and clubs). Seek these bad boys out in the Jewish district. You're obviously going to head to a famous budapest bath, but the biggest tip I can give you is to stay here for as long as possible 3 days was no where near enough. Affordable too.