We stayed at the Mercure Buda - very nice, good brekkie, pool, etc. near the castle. Check out for a list of the most popular with prices, reviews, etc.?
I stayed in the apparently 4 star Grand Hotel Hungaria on the Pest side and I wouldn't recommend it. It wasn't the cleanest, the got our booking mixed up, it was in a dodgy enough area and there was a bar in the hotel called the "Lady Finger Bar" that seemed to be a pick up point for prostitutes.
Definitely get a hotel on the Buda side, it's so much nicer.