I am not a resident there, and we probably have folks here that live much closer, but I have visited a lot both before and after Katrina....I guess it's been a year or so since my last trip though, and things keep changing!
I like to fly into Lakefront and get a courtesy car (or rental if I am staying a bit longer), drive down to the Quarter and walk around. My favorite place for a quick lunch is actually down by the Convention Center - Mullatta's serves a great blackened catfish with Crayfish Etuffe'...it's worth the Avgas to and from Houston! Not a fancy place, but good!
If you're going to stay overnight, there are lots of much posher restaurants down in the quarter - I have eaten at a few of them when out walking with friends, but unfortunately, those were trips (without an airplane or car involved!) where I was enjoying myself enough that they kind of blur together. Antone's? Does that ring a bell? Oh, and if you just want a quick snack, go by the French Market.
I remember reading that Lakefront's Tower just opened again this summer - it was down for a year and a half. I guess I need to make another trip to see how the recovery is coming.
Paul