Sziget Festival (www.szigetfestival.com), Budapest, 7 days in August
I'm from Croatia and was there first time in 2005 but i think it should be mentioned here. It's rock festival with some 20-30 stages and many many more things to do trough the whole day than just concerts at the evenig. There are up to 70 000, people camping and attending this big river island from all over Europe daily, and it is a great fun.
Well, actually there is a lot to do in Budapest (museums, pubs, concerts...), and several festivals all around the country.
I would say the most attractives towns are Szeged, Pécs, Györ... there are several festivals in spring and summer and the towns worth visiting too.
If you are interested in rom art, there are some opportunities to catch an interesting programm in those cities.
Others attractions are the termal baths, all around the country, with attractive prices and atmosphere.
Architecture and outlook of the cities is different, because of the diferrents stands of development, foreign influences and various artists who designed the buildings around the time. Some towns have inherited of mochees from the ottoman occupation... Interesting contrasts!