@PTI (pti) is a secret/closet foodie, and has lived down there for decades. He's got a blackbook of at least 50 places he can recommend, no matter what he says.
My 3 must-do's anytime I'm there as a turbo tourist
1.) Charbroiled Oysters (Drago's...Felix & Acme are good as well, but Drago GOAT)
2.) New Orleans BBQ Shrimp (pretty much anywhere. Mr B's had an excellent version on last trip)
3.) A great Po Boy w/ a classic side (Etouffee, Jam, etc)
Other than NYC, New Orleans is my favorite food town in the country...you really can't go wrong anywhere unless you are an idiot or you eat at a chain. It's just incredible pretty much everywhere.