Wow, you only have a weekend and you'll have to spend time and meals at wedding events? If you're a foodie, you can easily spend a week eating and drinking your way through New Orleans. ;D
If you're sticking with the Quarter, you HAVE to go to Pat O'Briens and get a hurricane in the patio at night - it's amazing. For food in the Quarter, there's breakfast at Brennan's and dinner at Antoine's. Both are pricey. Antoine's used to have lunch, which is more moderate. I think they still have some limited lunch hours. Right on the edge of the Quarter on Canal St., there's the Palace Cafe, another nice but relatively pricey place. A less pricey but classic New Orleans suggestion for the Quarter would be a muffelatta from Central Grocery. Cafe du Monde is also good. (I think Morning Call in Metairie has better coffee.) I don't think that much of Mother's, but I'm not a big fan of roast beef and their roast beef poor boy is supposed to be one of their better things. Acme Oyster house is another solid choice.
Beyond the Quarter, there's Commander's Palace, pricey but very nice. Jacque Imo's is a solid choice, too, but they don't take reservations unless you have a party of 5 or more and the wait can be HUGE. For a classic New Orleans place, there's New Orleans Food and Spirits - amazing corn and crawfish bisque and shrimp poor boys at a great price for lunch. It's in Lakeview, which suffered a lot of Katrina damage, but the restaurant was on the side of the levee that didn't give way. If you like Vietnamese and want to visit the West Bank, you can go to Kim Son. And if you want the best snow crab and spicy tuna in sushi, visit Kanno Sushi in Fat City.
Ah, New Orleans food ... YUM! If you're going to do seafood though, remember that right now oysters are not exactly in season so they won't be rancid or anything, but they just won't be particularly good.