I was in Budapest right after 9/11 on the Best of Eastern Europe trip. We seemed to have a fair amount of free time on all our stops. There's a beautiful opera house that was open for tours. And I remember an evening cruise on the river with commentary in every conceivable language directed to your earphones. The standout was the Great Synagogue which has been completely restored. Next to it is the Jewish Museum which at that time had a Chagall exhibit. Some people went to the baths, of which there are a wide variety. I remember that they require you to wear your bathing suit.
Something to purchase if you're interested in really good skin care products is Helia-D. It's produced in Hungary and, as far as I know, isn't available anywhere else. I bought some there for myself and a friend, and when it was all used up depended on other friends going to Hungary. When I was on the Grand European Rivers trip, our PD who was Hungarian arranged for a friend to buy me two jars and bring them to the ship when we stopped in Budapest. Although I have since found it available on the Internet.