If you haven't been to New Orleans, there is not one thing I can tell you to experience. Everyone gets something different out of this city.
Regardless, due to Katrina you will need to know what's open when you're down there. You can do it one of two ways:
1) Prior to leaving, you can go to QuarterCrawl.Com and look and see what's open.
2) You can ask your hotel for the lastest copy of "French Quarter Pocket Guide." It's a handy guide of what's open right now in the French Quarter and Marigny. It is published every two weeks on Friday. I found my copy at the front desk of my hotel. You can also find them at various bars, shops and restaurants.
The pocket guide has addresses, phone numbers and maps inside of it. It's a very handy thing to have while deciding where to go.