In Buda, across the cobblestone road from the Hilton, is the Hungarian wine museum. Wonderful stuff (yes, you sample the exhibits).

In terms of mineral spas, choose from several public bath options. You will want to choose co-ed or not depending on your proclivities -- each bath changes by the day of the week.

Near the Marriott in Pest is a wonderful folkcraft store on two levels -- it's on the Vaci utca.