I've had reason to be in New Orleans quite a bit for business during the past year. In my opinion, Stella's has been consistently the best restaurant I've eaten at in the city. I'd put it up against the top restaurants around the country. I never hear much local love for Stella's, and I think (a lot of) you are missing out on a treasure.
My second favorite has been Clancy's. The food is solid (although always, strangely a little too salty). But the atmosphere and location is great. For an out-of-towner, it feels like a "discovery."
Other places I have enjoyed quite a bit:
Po Boys at Hank's Market on St. Claude
Jacques Imo's (food was eh, but atmosphere is fun)
Peristyle (feels like dinner at Miss Havisham's)
Commander's (talk about not living up to a reputation)
Most other Brennan-clan endeavors (with the exception of lunch at Mr. B's)
I'd be intersted in anyone else's recommendations given the list above. I've never gone to K-Paul's, but still feel like I would/should.