Budapest is one of those places where if I had the choice of going there or going to Prague, I'd pick Prague. While they are both beautiful, Prague is livelier.
I tend to like to travel to places in off-season and Budapest was dismal in winter. The Danube is really brown and since there aren't so many tourists in winter, alot of things weren't open or the lights weren't on. Summer was much much better and Budapest comes to life.
It's definitely a city to see at least once and with it's popularity, I would think you'd be able to work out inexpensive ways to do it.