Sorry for the delay, but I just got back to NYC. Apropos of your posting awhile ago, the Hungarian place I was thinking of is at the First Hungarian Literary Society (323 East 79th Street, 288-0615). There had been a NYT article on the club, which mentioned the restaurant aspect as well.
I suspect the diners are generally members, who seem to be largely older emigres, and I suspect they hang out playing cards at the large tables the rest of the time. It's open to the public, however (although I was a bit self-conscious to try it at the time), and I believe they have a reasonable prix-fixe. Please report back if you go. (It has to be better than Mocca.)