Went there last year for a couple of days, for a wedding.
Didn't get too much sight seeing done, but the pinball museum was great, was the 1st thing I did when I had free time.
I stayed at the Danubius Hotel Gellert, very cheap room, booked well in advance. I never got round to trying out the spa sadly, but I did try the Szechenyi baths, which was well worth the trip on the metro.
Museum wise, I hit up the Hungarian National Museum and Buda Castle. Just check opening times, I went there on a Monday, and I was a little bit miffed after climbing all those bloody steps to find the museum and art gallary closed.
Public transport was pretty good, I just bought myself 1 day travel cards and got about on the metro and the trams, very easy.
Food and drink wise, again pretty good, thankfully I had a Hungarian friend to help me out there.