We more prefer the free activities where possible. There is a free walking tour (tip encouraged) that starts at 10:30amd or 2:30pm that gets you to all the major sites and some history too. If you do the morning tour, they also have a free tour at 3:30. Depending on the day, it will be either the Communist Tour or Jewish tour. We've done several walking tours in Eastern Europe and found this group to be the best organized.
After the walking tour, the House of Terror is an eye opening, educational museum too.
If you're there in the evening, when it's a little cooler, a traditional bath house is a great experience. We went to Lukas, which is only 1700 HUF after 6:30pm over 8 years ago