The English language blog Chew.hu has a solid Top 33: http://www.chew.hu/top33.html.
The listings have links to helpful embedded Google maps. It pretty much covers the array of available restaurants here and doesn't acknowledge most hotel restaurants. There's also no representation of the kitsch Hungarian gypsy music place in the list that some enjoy.
Liszt Ferenc ter is pretty much a sea of mediocrity, although still a great location for outdoor relaxing. Some people still regard Menza for its good prices and solid food, but many are turned off by their unreliable wait staff.
A nearby place that I highly recommend is Klassz, which is near Liszt ter on Andrássy. Other nearby good places are Balettcipő and Cafe Bouchon. (however none of the above mentioned places have a great outdoor set up)