A few of my favorites--
Coquette on Magazine. I think their lunch is second to none, but dinner is delicious as well. Lunch has a 3-course special for like 22 bucks or something. Order an additional desert and you'll be really pleased with your decision.
Chinny is right about Jacques imo's. Great stuff. Load up on their corn muffins. So good. When you go, make sure that you finish around 930-10 and then head next door to
The Maple Leaf. That place has kick-*** live music every night of the week. See some brass music or funk there, if you can. Those two places in one night is pretty much reason number one that some people live in New Orleans.
Head to Bullet's sports bar (bigdub's bar) in the 7th ward on Tuesday night. Kermit Ruffins and his band start around 6 or 7 and absolutely crush it. You can get great BBQ or cajun food on site. I drive 15 minutes every Tuesday for this show, and it's worth it every week. Shoot me a message before you come and I'll save you a spot at our table if you want.
Make sure you see some live music at frenchman. Blue Nile and Snug Harbour are two of my favorites.
Best of luck. It's a great city. Avoid the tourist traps and bourbon (except one or two nights) and you just might learn what it means to love New Orleans.