There's a place in the Garden District called "Upperline". The food has always been fabulous & the service very friendly & efficient without being obtrusive. Prices are in line (a little high) but the place is definitely worth it!!!
I've been there several times, but not for about three years. Whenever I'm in NO, I make it a point to go there. I'm from Alaska, so it is a special treat after a long trip.
Take the trolley from the Quarter. It's a lot of fun.
http://www.upperline.com/