Budapest is absolutely outstanding. I was there for a few days last March and was sad to have to leave. Along with the major sights (touring Parliament, Museum of Terror, walking up Andrassy Ut, etc.), there's a great pastry shop up on Castle Hill called Ruszwurm and I also enjoyed people watching/coffee drinking at Central Kavehaz. I also did a sidetrip up to Szentendre and enjoyed wandering around.

Lodging-wise, I stayed in a hostel but did duck into the Gresham Palace for a few moments. Seemed pretty luxe and I felt too poor to be walking around those digs, ha ha. Finally, the bus/subway from the airport was easy enough but you'll need some coins to buy bus tickets from the dispensers and once you get to the subway station regular tickets/passes are easy enough to get from vendors. They operate on a sort of honor system, but have inspectors roaming around so make sure you keep your ticket on you.