Fatál Restaurant
Fatál (not to be mistaken by the femme fatale, since "fatál" is a Hungarian word meaning "wooden plate") is the only restaurant in the area where you can surely have a meal after 22:00 (it is open till 02:00). Though the place is a bit touristy, the portions are big and food is tasty, and the beer is quite inexpensive (for this particular area).
V. Pintér utca, 2