I sincerely hope this doesn't come across as arrogant, and I know I may be a bit late, but in light of all the "I'm coming in town, where should I eat posts?" I thought I'd do a quick (okay, long) list of places I'd eat at, as someone from New Orleans (now an ex-pat in Northern VA).....
Here goes. Feel free to fire back at my choices!
If I woke up in Midcity, or ended up there before Jazz Fest, I'd head over to West End for breakfast/lunch at Russell's Marina Grill (home of the original bloomin' onion - check the menu at Outback for the credit). Lunch would probably be a shrimp or french fry po-boy at Parkway Bakery, washed down with an Abita Beer, and finished off with a lemon Hubig's pie. Alternatively, I might stop by Liuzza's for a frosty mug of beer and some chicken parmesan, or at an appetizer of those eggplant medallions with red gravy (it's red sauce or pasta sauce in the rest of the world, but you ain't in the rest of the world). Liuzza's is also a great place after the Fest, though truthfully the time between the end of the Fest and whatever evening show you go see really ought to be a friend's house (new or old) for a bowl of gumbo or some crawfish.
A side note here: if you go to New Orleans for Jazz Fest, try to get out to a club at least one night. By club, I mean hole in the wall, not velvet-rope. I'm thinking Carrollton Station, Snug Harbor, d.b.a. You'll hear great New Orleans music any time of year, but especially during Jazz Fest. I could go on forever here, but check out Paul Sanchez, John Boutte, or Shamar Allen if you see any of them listed somewhere during your stay.
If I was at a friend's house in RiverBend, I might eat breakfast at Camelia Grill. Lunch would be a shrimp po-boy (there's a theme here) at Domilicis, which is Uptown, but close enough. I might stop in at the Columns (site of filming for Pretty Baby, an early Brooke Shields movie) for a mint julep, or just keep going back to River Bend for a beer, raw oysters, and cheese fries at Cooter Brown's. A casual dinner can be found at Louisiana Pizza Kitchen (the alligator sausage pizza is worth trying); a more upscale choice would be Mat & Naddie's. If you don't mind the wait, head over to Jacques-Imo's for dinner. The wait is crazy by New Orleans standards, and the place looks like nothing much, but I'm tellin' you, it's a little slice of heaven, New Orleans style.
Uptown for breakfast, my favorite is Bluebird. Grab a Times-Picayune out front and read the local news while waiting in line. Yellow grits may not be traditional New Orleans, but whatever they put in those things, they are terrific. Try the omelet with sausage, jack cheese, and green chlis. This is precisely how I started off the first day of Jazz Fest 2008 (4/25). Another choice for breakfast or lunch is Joey K's. Lunch could be Cafe Rani (if it's re-opened since the storm). Dinner might be Clancy's, or the Upperline. For something special, I still think it's Commander's Palace. This would be a great Sunday brunch choice as well.
In the French Quarter, grab beignets at Cafe du Monde. Then, if you still need more sugar, get a couple different brands of pralines from the shops just past Cafe du Monde, grab another cup of coffee, and go on up to the Moonwalk overlooking the river. Find a bench, settle in, and have a taste test while enjoying the view. Here's a hint: buy all you want, but Aunt Sally's is the best (other than my mom's). If it's Sunday brunch, try the Court of Two Sisters. I always thought this place was too touristy until I ate there a couple of Sundays ago after a wedding. The Sunday brunch was terrific. Where else can you eat grillades and grits, an omelet, and boiled crawfish, all at the same time?
When you're done with all that, head over to Cafe Maspero's or Central Grocery for lunch; order a muffuletta at either one (it's basically your only choice at Central Grocery, with good reason). Disclaimer: the good folks who own Central Grocery, the Tusa's, are friends of my family's, but they are good people, and their muffulletta is the best in the city. This last statement about the best in the city nearly cost me my girlfriend once, but if you're going to lose the one you love, do it arguing over New Orleans food.
For dinner, hit the Gumbo Shop for casual, but good. I know some will say it's touristy, and it is, but it's also local. For years, my family Christmas tradition has been to go to the Cathedral for mass, then to the Gumbo Shop for dinner. If its' good enough for a restaurant family in New Orleans (we owned Teddy's Grill in Gentilly until the storm killed it), it's good enough. The chicken and sausage gumbo is the best of their offerings, along with the corn macque choux. [True story: two years ago, we went to the Gumbo Shop on Mardi Gras night for dinner. There was a woman eating dinner there wearing nothing but paint. It wasn't pleasant.]
A cheap option on the other end of the Quarter is Port O' Call. Great burgers, but the pizza is also good, too. Order a Huma Huma or a Blue Hawaiian, but eat something first! You could also head over into the Marigny and check out Marigny Brasserie, which is a little pricey but very good.
If you want slightly more upscale than Gumbo Shop, head over to Irene's, but try to make a reservation, or you'll wait a long time. Fancier still is Mr. B's Bistro. I love the gumbo ya-ya; it's the first dish I ever had that brought to mind the word 'orgasmic'. I was 20-something, and it was Valentine's Day, but still and all........I've never been a big fan of Arnaud's or Antoine's, or even Galatoire's, except for the tradition. If you are a local, they can all be excellent, but if you're not, I think the service and experience may not be worth the cost. If you don't mind spending some dollars, I love K-Paul's, but make a reservation and eat upstairs. Blackened anything will be great, as will the muffins or breads they bring out to start the meal. The gumbo here is pretty good, too.
Of course, the thing I didn't mention is Jazz Fest itself. Eat. A lot. Try different things. It' pretty much all terrific, and very representative of New Orleans. When you want a sno-ball, (and no, it's not the same thing as a snow-cone - don't get me started), go to the Plum Street Sno-Ball stand towards the Gentilly Stage. While you're at it, grab a stick of Roman Taffy from the guy in the carriage to the left of the stand a ways. You'll be awash in several New Orleans traditions all at once!
Enjoy your time in the city. Have some fun, but go see the destruction, too. It's important. Television doesn't capture the vastness of the damage. It also doesn't capture the feeling of rebirth creeping back in. I don't live there now, but I do own a house in Midcity, and New Orleans will always be my home. I hope to get back someday.
Peace and gumbo y'all....