My main reason of traveling to Hungary and Budapest was Sziget, one of the biggest music festivals in Europe. No, actually the reason was that a big group of friends was going there, and I had never been to Budapest, and I figured we would have a great time there. Which we had.
We spent seven nights in Budapest, and on five of them we visited the festival area on a large island in Donau. I saw the performances of Natalie Imbruglia (nice but not memorable), Juliette and the Licks (great act including her stage-diving but I cannot remember her songs either), and Accept (strong German metal). I also heard a small piece of Korn (who had some technical problems), glimpses of Sentenced (should have seen more) and Turbonegro, half an hour of Opeth (somehow didn't appeal to me live), and also some Fishbone. I should and could have seen more bands, but it is quite tiring and after a while you'll happily change the crowds to some gyros on plate and a beer or two with friends.
We also took some time to explore the city of Budapest. We saw quite a few museums: The agricultural museum in the city park (not that much stuff, but stuffed pigs and a picture of a bull with big balls come to my mind), House of Terror (former headquarters and torture chambers of security services now displaying its past through interesting artistic displays and decoration), the Unicum museum (history of a local liquor factory, with tastings of course), and back to the more traditional national and military museums (swords, guns, harnesses and the like). The museums had only part of their texts in English, which limited the amount of information received. However, many of them didn't have entrance fees, so their value for price leaves nothing to complain about.
Other tourist attractions we experienced include the market hall (goose liver paste, anyone?) and the Buda fortress hill and the labyrinth underneath it (maybe not worth the entrance fee, but interesting nevertheless). I found the Buda side of the city more exciting, old and mysterious. Narrow alleys full of stories. The Pest side was more modern, business-oriented and rational.
Our short visit left a lot more to see, such as spas, opera, statue park, more museums. Budapest could be worth visiting again, but as a friend of mine said, there is a lot to see in the world and our time and money are limited.