1. Scott already mentioned Capedeville
2. Yo Mama's Bar & Grill on St. Peter Street. Best burgers ever...at least when I went there
3. +1 on Rickster's Cafe Beignet recommendation
4. Lucky Dogs. Located all over the FQ. Great drunk food. Seriously,after a night of daiquiri's or whatever you're drinking, you don't care what's in them
5. Acme Oyster House on Iberville. If you like oysters and can deal with a line.
6. If you're willing to travel a little: Juan's Flying Burrito on Magazine St
There's a million restaurants in NOLA so take your pick. You need to watch out though, especially in the Quarter. Some bars/restaurants are just total tourist traps Read some reviews before you go.