I'd go for Budapest, went there in June with some clients of mine who come form there and loved it. You can also do cheap days out to Vienna and Bratislava by train. It's very cheap and loads to do.
We stayed in the Art'otel by the Danube on the Buda side (Castle, St Mattius Church, Palace, Gellert Spa baths side) and the main town is in Pest over the River with the stunning parliament and bascilica.
http://www.artotel.hu/budapest/budapest.html
They have a wonderful zoo and caves if you travel a bit further out.
It's quite big (compared to more walkable places like Prague and Amsterdam) but they have a great metro system.
I'd highly recomment the Sir Lancelot restaurant - definitely a night to remember!
http://www.sirlancelot.hu/
You'd definitely have a lot to see and could go by hydrafoil up trhe Danube to Vienna (for the wonderful Patisseries - we have a fantastic day there - 3 hours on the very cheap train each way) or Bratislava. Think the hydrafoil is about 5 hours to Vienna.
Also easily reachable are...
Szentendre -
http://www.budapesthotels.com/touristguide/pro grams/szentendre.asp
and
Visegrad -
http://www.budapest.com/excursions-hungary/vis egrad-hungary.htm
I've been to Bucharest doing youth work and have to say I wouldn't go as a holiday.
Prague is lovely though very pricey round the tourist areas. Hotel wise I stayed at the 987 Design which was lovely and just out from Wenceslas Sq with som