We're not local, like Doc and Family, above, but we do make frequent day trips, since we're only a couple of hours away.
Windsor Court is simply spectacular. As part of the Orient Express family of hotels, it has a cosmopolitan, international feel - you know, that sort of British veneer that we just don't get much of in the states. (I might mention, too, that we stayed at Charleston Place - another Orient property - for our anniversary in July on points, and it was the stuff of legends, too.)
Windsor Court isn't actually in the Quarter, rather on the fringes, but a pleasant walk to wherever you want to go. If you want a full dose of debauchery, then Mardi Gras is the ticket, but there's stuff going on all the time. But, during the heat of the summer, the humidity in NO is so thick you feel like you're swimming - you almost need an oxygen tank to get around! Nink's right about walking - it's the way to go. Like any large city, though, ask your hotel staff where it's best to avoid late at night.
I peeked in on the Quarter House on one visit, and wasn't too impressed. Windsor Court sets the bar way on up there.
Re: Food. Yeah, throw diet and health concerns out the window for your stay. Try Emeril's - some locals say it's become too touristy, but it IS his flagship restaurant, and worth doing. If I had to choose one eatery for a last meal in NO, I'd have to go with Commander's Palace. Culinary heaven.
I could go on. I'm about to salivate all over the keyboard even as I type.