Budapest has a number of great hotels. Both the Marriot and Hyatt are excellent and are located near the Danube. They are easily accesible to public transportation, great shopping at the Vaci Utca, and of course, the Gerbaud Cafe!!!!.
There is a new Hilton that will be open soon attached to the new Western Mall, which is very close to great shopping and public transportation.
Also close to this Hilton is the Family Hotel, which is apartment style accomodations, and very reasonable.
If you are interested in a great spa the new Helia Hotel has wonderful thermal waters and is extremely reasonable, just not conveniently located. It is very clean, unlike the Gellert which is a wonderful hotel but has that centuries old smell from the waters.
Hope this helps, I have much family still in Budapest, so feel free to e-mail, if you have any questions.