I second Commander's Palace. the jazz brunch on the weekends is SO much fun. they put balloons all over the place and jazz bands go room to room. (it's a big old mansion and simply beautiful)
One thing that's really fun (if it's a nice day) go to Central Grocery and get a muffaletta. You can walk to the river ( right across the street ) and sit and eat and just watch the ships go down the Mississippi. Also, Mother's Restaurant is awesome. it's a total hole in the wall but truly the BEST basic food you'll ever eat. The line outside the restaurant is wrapped around the block hours before they open and you can't sit down until you have your food. ( or they'll yell at you) They're fried oyster po-boys are amazing. (and oddly enough, their corned beef and cabbage is to die for)
Acme Oyster house is a MUST DO if you like anything oysters. Just sit at the bar and order some Dixie beer and oysters on the 1/2 shell.

Cafe Du Monde has the greatest beignets ever. you can go any time of day. (avoid dark clothing because you WILL be covered with yummy powdered sugar)
the alligator swamp tours are really alot of fun. A must do right in the city of New Orleans is the Aquarium . it took a hit during Katrina and is back and better. It's just beautiful and right on the Mississippi. They have wonderful IMAX films too. That's a good few hours of a day and well worth it.
Canal Street has great shops and Jax Brewery has great shops.
Try to go into St. Louis Cathedral. It's right in in Jackson Square (Cafe Du Monde is across the street). it's truly such a beautiful old Catholic church. Sometimes you can catch a choir concert at night and it's really nice. ( at Christmas they do that alot)
You should also take a walk down Bourbon Street and go to Pat O'Briens for a signature Hurricane Drink. be careful...they're bite is worse than their bark !!

You'll be on the floor if you have too many !!!
I'm afraid I've gone on rambling....sorry !!!
I hope you have fun !!!