$
Budget
There are many smaller shops, Chinese restaurants with cheap food.Julia Chinese restaurant menus from 490HUF in the Buza ter behind the Marketplace building and a cheap Chinese restaurant opposite Szinvapark are examples. Fozelekbars offer Hungarian type of food for around 400-500HUF, there is one in the Szivapark Food Court.
$$$
Top end
Cafe du Boucher (http://www.belgianbeercafe.hu/) is an excellent eatery. It is a Belgian Beer Cafe with many different Belgian Beers and Cigars. Food is excellent and English is spoken. Make sure you leave a good tip so that the bell is rung as you leave the place.