I visited my brother last month in New Orleans. First time I had been in the city in many years.
You have received many excellent recommendations on things to do, see, and eat.
Let me offer three must's from my recent visit:
(1) Visit the World War II museum. The displays rival the Smithsonian's.
(2) Eat at Commanders Palace. A little pricey but well worth the visit.
(3) A biegnet and cafe au lait at Cafe Du Monde.
For those traveling to New Orleans. Enjoy your visit, spend $$$ the economy needs it, and don't be offended by Tiger Bait chants.

Take it in the spirit it is intended and chances are you will be offered food and beverage.