A great way to spend a few hours, and get some great exercise, is walking around Gellert Hill [Budapest, Gellért-hegy, 1118 Hungary]. If you’re staying on the Pest side, I would recommend walking over Liberty bridge to get there. It really adds to the whole experience. There are a number of bridges from connecting Buda and Pest. The elegant green Liberty Bridge is pedestrian friendly and less than a quarter of a mile long.
As you make your way from Pest to Buda you begin to see the sights of Gellert Hill. You may spot the monument at the top as you stop to take some pictures, just be careful – it’s windy out in the center.
However, as you might intelligently guess from the name, it is simply a church within a cave. Unless you are going for a service, or really into religious buildings, you might just want to enjoy its beauty from the outside and skip the nominal fee for entering. There are many beautiful spots along the hike up the hill to take a moment and breathe in the scenery.