The closest traditional Hungarian restaurant that also happens to have a very good reputation is called Pesti vendéglő. It is just in the next street:
Guests of 7x24 Central Hostel get a voucher that gives them a 10% discount at this restaurant.
So if you’d like to taste Hungarian goulash (stew), goose leg or Gypsy style pork, try Pesti vendéglő in Paulay Street. Take a look at their list of Hungarian specialities.