Budapest is an amazing city, during the day there is lots to go and see and explore including the castillion, the baths and the market. There are plenty of good restaurants too although some of them can be pricey in the central tourist area. Night time the ruin bars come alive and are lots of fun to visit and explore although it can get quite warm inside. Heroes square and one of the baths is quite a walk away but definitely worth a visit. In general a very cheap area to buy food and drink.
Insider Tip:Try to book a "spa party" at one of the baths they're a lot of fun.