How old are your kids? I live about an hour away. A decade or two ago I could tell you about the great bars, but now I can only tell you about the kid friendly activities! The zoo is amazing, we like it so much better than the San Diego and National Zoos. The aquarium and insectarium are nice, also. If your kids are younger, city park has a kiddie area that younger kids love. The Mardi Gras World museum is fun.
Take your time at the French Quarter festival... Sample all of the foods and drinks, try an Abita beer, people watching in NO is awesome! There are usually artists in Jackson Square. Ride the streetcar through the garden district. St. Louis cathedral is beautiful. DH loves the WWii museum, my kids like playing in the bunkers outside there.
I wouldn't worry about food too much, most restaurants will be great. I think Commanders is overrated, and Acme is a tourist focused place, so save your money and time. Camellia Grill is also heavily visited by tourists, at breakfast there will be a line out the door, but we still like it. You can sit at the counter and the cooks will talk to you, they're usually funny and the food is good.
And it may seem weird, but the cemeteries are really nice, you should definitely go to at least one. I had a friend from college (in PA) come home with me for spring break once, and she was in awe of the tombs/ vaults... It never occurred to me that all cemeteries didn't use them!
