Jazzgarden is a (no big surprise) jazz restaurant in Budapest, located near the Liberty Bridge and Pampas Steakhouse. It is normally open from Monday-Saturday, and every evening there is some kind of live jazz event going on. This event has a small entry fee, but it is also possible to sit in another room without paying (you will still hear the jazzmusic). The interior makes you feel as if you sit in a garden (even though you sit in a basement), so the atmosphere of the restaurant is great.
The food at Jazzgarden is not very expensive, and it would probably not win any gastronomical prices, but if you like jazz and food this might be the combination you are looking for.
Address: 1053. Budapest, Veres Pálné u. 44/a