Honestly, we could both see ourselves living here for a while because there are so many things to do in Budapest, and lots of them are free (or cheap!). Budapest has character, history and is quite affordable compared to many other European cities. If you’re planning travels to Hungary or anywhere in Eastern Europe, you must visit Budapest. We'll explain why we fell in love with this city and how you will too with the top free and cheap things to do in Budapest. Pest = New TownEast side of the river, this area is more modern and has a more lively nightlife scene; lots of restaurants and cafes.