If you are any kind of history buff at all, do not miss the National D-Day museum. It is in the old factory where they made the Higgins boats (the landing craft for D-Day). It is one of the best I've been to.
Oh, and eat well. Commander's Palace, Mothers, Emeril's, Cochon, Velvet Cactus, Mulate's, Cafe Du Monde, the Central Grocery, the list goes on and on...