Some of my recommendations for food:
Mother's for Red Beans & Rice, Ferdi's Special Po' Boy
Johnny's Po' Boys for other kinds of Po' Boys
Pascal's Manale for BBQ Shrimp, Old N'awlins as a close second
Progress Grocery is now closed, but whoever is in their place (Is it Julia's?) still makes a great Muffaletta. 915 Decatur St.
Napoleon's if you want your Muffalettas heated
K-Paul's for great upscale Creole and Cajun
Nola for the same
Commander's Palace for a one-in-a-lifetime dining experience. Go at lunch to save money and you can also go casual at lunch, not at dinner
New Orleans School of Cooking for an entertaining cooking class and a decent classic lunch of Jambalaya, Gumbo, Bread Pudding and Pralines
Some fun things to do:
Shopping at the French Market. Arts, Crafts, T-shirts, and more food to take home
A Garden District Tour
A Riverboat Ride
Walk, walk, walk through the French Quarter ("Catch a horse-drawn carriage, ride it down to Basin Street. In the old French Quarter, you know ya got ta use your feet. Dixieland and Hambone, I'm goin' back where I belong. I know what it means to miss New Orleans.")
Check out Mardi Gras World, the WWII Museum, the Cabildo and the Civil War Museum
Perhaps gambling at Harrahs, if you want to just lose your money (never seem to win there)
Check out the bars -- they all have live music. I particularly like the Funky Butt, as well as a bunch of them on Bourbon St. Just walk down Bourbon, and stop in wherever the music catches your attention
Sid-Mar's (near the lake): Possibly the best shrimp, crab and oysters in town, and at reasonable prices. Their oyster soup and seafood gumbo are legendary with locals.
Gumbo Shop (in the Quarter): Great gumbo, good shrimp remoulade, and decent crawfish pie.
Dooky Chase (mid-city): Homestyle creole cooking with a heavy African influence. Best dishes are Shrimp Dooky, Creole gumbo, Shrimp Clemenceau, Stuffed shrimp, Crawfish etouffee, Breast of chicken a la Dooky (stuffed with oysters and topped with marchand de vin sauce). Very good fried chicken.
Galatoire's (in the Quarter): People rave about the Trout Meuniere, but also a classic, "old-time" restaurant in the tradition of Antoine's for classic New Orleans creole preparations. Consider Shrimp remoulade, Crabmeat maison, Canape Lorenzo, Oysters Rockefeller or Oysters en brochette. Also the steak bearnaise is great. Jacket required.
Antoine's (in the Quarter): This restaurant is splurge material only. It is one of the oldest operating restaurants in the U.S., and claims to be the oldest. They invented Oysters Rockefeller. There is better food in New Orleans, but it is done very well here, and is worth it once for the experience. Classic creole/french cuisine and classic presentation. Jackets required, and quite expensive.
I still think that the Wyndham (used to be the Westin) Riverview Room's Sunday Brunch is the best buffet brunch in town, with great food, good music and a spectacular view. The Wyndham Brunch, while a bit pricey, is worth the splurge for me. I love to sit there, listening to Louis Armstrong type music, watching the river and the Quarter from two-story high windows, and eating some very nice (though not spectacular) food.
Hurricanes at Pat O'Briens, which is a classic tourist thing to do. I Pre-tipped our waitress a few bucks, who then set up a table for us right next to the flaming fountain in the courtyard, and we had a delightful time getting blasted on one hurricane each (I don't recommend more, unless you plan on getting so drunk and sick that you can't walk).
We ate at the Redfish Grill, because it was the only thing still open after our Ghost Walk. Food was pretty much unremarkable. EXCEPT the Double Chocolate Bread Pudding, which consisted of bread pudding infused with chocolate, and covered in a dark chocolate sauce and a white chocolate sauce. One of my cousins, who said that she does not like bread pudding, was running her finger along the empty plate, trying to get whatever last morsels she could scrape up. So, go there for the dessert, but not the dinner.
You could read "A Confederacy of Dunces," (Pulitzer prize-winning novel set in New Orleans) and see whether that makes you crave a Lucky Dog (it makes a lot of people crave them for some reason). Then you could get a dirt-cheap meal by buying a Lucky Dog off the carts in the streets of the Quarter. Felix Oyster House (less famous than Acme Oyster House, but better, fresher food) has a good raw bar, and decent casual seafood selections (also casual, low to medium priced). Ralph & Cacoo's (about the quality level of Macaroni Grill) makes some of the best Shrimp Remoulade in town. But most of their other offerings are mediocre, unless you like blackened gator. Their blackened gator is quite good.
The Quarter Scene Restaurant makes a great Caribbean Waffle (Waffle covered with Whipped Cream, chopped apples, mangoes, melon, strawberries, pecans, and other various fruits and nuts) and has very good coffee. At about Burgundy and Dumaine, the breakfasts there are quite good.