Went to Budapest recently and that was great, also did a day trip to Vienna on the train. Bratislava is also very easily reachable.
Budapest is nice and cheap, lots of culture and nice places to eat and drink (Sir Lancelot restaurant where my hungarian friends took us is a MUST! -
http://www.sirlancelot.hu/ ).
They have a great zoo (http://www.zoobudapest.com/english), caves (http://www.budapestinfo.hu/en/things_to_see/caves) , castle, lovely churches, famous spa baths (http://www.budapestinfo.hu/en/things_to_see/thermal_baths), nice days trips eg Visegrad (http://en.wikipedia.org/wiki/Visegr%C3%A1d) and Szentendre (http://www.talkingcities.co.uk/budapest_pages/sights_daytrips.htm).
Amsterdam and Prague are great but more pricy.
Bratislava is a possible as you could use it as a cheap base and have day trips to Vienna and Budapest. They are all linked by the Danube so you can go by boat as well as train, takes longer but more scenic.