My opinion is do a ship excursion or go straight to the airport. Although I l Iove NOLA, things are rough there now. I won't hand over my luggage with limited time. Could be a real hassle. Most restaurants are not worth the prices they are charging.
But if you really want to be adventurous and aren't doing a ship excursion, the only other thing might be to rent a car, if you get out of downtown there restaurants, etc.
But I would go to airport