I went twice last year and I'm going back next month. The Quarter is pretty safe (standard city rules still apply) because they need the tourist dollars badly.
Eats:
Cafe Maspero (Toulouse & Decatur): fried seafood platter is enormous (and relatively inexpensive), red beans and rice are quality, and $1 PBR draft.
Port of Call (Esplanade & Dauphine): get a burger...that is all.
Central Grocery (Decatur near the French Market): the original Mufaletta...you have to have one.
There are as many restaurants catering to as many budgets as you can imagine. Just drop in some shady looking place and give it a shot.
Drinks: During the day almost every bar on Bourbon runs a variation of the "Buy 1 get 2 Free" special. You'll be drunk quickly. Avoid the gimmick drinks (handgranade at Tropical Isle/Pat O's Hurricane)...they are overpriced and watered down.
Off the beaten path drinking: Ryan's Irish Pub, Chart Room, Napoleon House (a little more uppity, so don't make this one a late night drunk stop).
Strip Bars: Just avoid Big Daddy's...I know it's a landmark, but the talent is untalented and the one drink minimum is a way overpriced small glass of warm beer.
That's what I've got off the top of my head.