Some very good suggestions. Nice job by all.
Al's suggestion of the Court of Two Sisters is a good one. .
I know the owners of this establishment, and there has been recent undeserved tragedy in the family. If you are interested in buffet style eating, it is a very good choice. Brunch here would be a good start for Sunday's festivities.
Mother's in unbeatable for lunch. A Ralph, which is a Ferdi w/ cheese, is what I normally have.
Oysters at Dragos are very good, and it is located in your hotel. Plus, I like to support this family because they served 75,000 free hot meals following Katrina.
Acme has great charbroiled and raw oysters to go along with cold beer.
Pascal's Manale is an old staple. Known for BBQ shrimp and oysters. I would recommend, but you will be cabbing it.
Galatoire's is great, but jacket is required after 5pm and on Sundays. Mr. B's is a delicious smart casual fine dining establishment, and is just a walk away from the Hilton.
A GREAT restaurant, if you are into seafood, is GW Fins. Fresh, wonderfully prepared seafood. Definite favorite of mine. Dress is smart casual.
If you and your wife want Italian that is local favorite, then Irene's in the heart of the quarter is a great choice. As i recall, there are no reservations, so go early. I know waiter there, so let me know if you decide you want to try this place.