I just returned from N.O. (my first trip there in over 8 years) and have several recommedations.
Day 1: (lunch)The Napoleon House (Chartres/St. Louis) spectacular atmosphere, great (enormous) Muffaletta and Italian sausage po'boys.
(dinner) Herbsaint (St. Charles) By far, my favorite meal in N.O. The atmosphere is casual-chic and not touristy at all. Great French food. A must try is the Banana Butter Tart.
Day 2: Brennan's (Royal) Toursity, but the strawberry crepes were amazing!
Day 3: Court of 2 Sisters (Royal) disappointing... pricey, surly waitstaff, trout overcooked.
Day 4: Commander's Palace (Garden District) I was a bit skeptical since it is a tourist destination but it was fantastic! The tuna salad is a standout with sashimi grade tuna and a dressing that is very unique.