Since the
French Quarter is one of the most popular parts of New Orleans there are lots of restaurants to choose from.
Some of the highest recommended are :-
Brennans
7 on Fulton
The Embers Steak House
The Plimsoll Club
Andrea's
Dominiques
I could name many many more. If you would like to tell me the type of cuisine you like i could narrow the list down a little. Also you havent mentioned where you are from but if you are taking a trip to New Orleans you have to check out
Bourbon Street and the
French Market.