Vakvarjú is a restaurant chain. You can check their locations here: Vakvarjú Locations in this website you will be directed to the sub-website of each location once you press „Belépés” – which stands for „Enter”. The sub-websites have English versions including the menu of the particular location.
Each location has its own menu and design. The images below are from the „Paulay Ede St.” restaurant.
This image is from the Érem St. restaurant:
Vakvarjú is popular among locals. They serve varied food and their menu changes almost monthly. It is probable that they will have some Hungarian, or Hungarian style dishes, if that is what you are looking for.
As they have locations in the city centre as well, you might combine visiting them with your sightseeing trip of the city centre.
In the evening I recommend you make a reservation, no matter which location you visit, as they may well be booked out.