I'm told that if you're in Budapest, you should include Lake Balaton and the towns of Tihany & Keszthely, which are very interesting. The view of Lake Balaton from Tihany above it is supposed to be beautiful and there is a picnic area. There are also medieval bldgs. I hear the area is loaded with B& B's & inns. Keszthely is a lakeside summer resort with museums and a flea market. And they say that the town of Pecs is an absolute treasure.
I did not visit the above towns as I sampled the spas and couldn't tear myself away. The thermal waters were simply fantastic; I felt like a million dollars! Try to arrange a visit to a thermal spa even for a night. It would certainly be relaxing.