Ooooh, this question makes me hungry.  I'll share my top three that are in or walking distance from the French Quarters!

Breakfast: Surrey's Juice Bar -- I went there twice during a weekend trip once.  It's that good!  Must order their shrimp and grits and their bananas fosters bread pudding.  If it makes you feel any better about your gluttonous decisions, you can order juice in creative combos of fresh fruits and veggies to wash it down.Brunch/Lunch: Stanley is the place to get the best eggs benedict!  They have really creative ones, including a soft shell one.  Their corned hash was also really good.Dinner: Acme Oyster House is the place to be.  Randomly stumbled upon this place when I was starving, noticed a line and got curious, so I went.  So glad I did.  Very first place I ever had chargrilled oysters and my travel buddy and I ended up ordering an extra dozen after we finished our first.  "Boo fries", which is their version of poutine, were good, too.  This place is divey and awesome.As a bonus, I'm throwing in Casamento's, also for chargrilled oysters.  It's in the Garden District, and they have great seafood sandwiches on top of having great oysters!

Hi Aaron!  I'll quickly try to put some things together, off the top of my head, as I'm heading out of town myself.  Some are nice and expensive and others very tasty and affordable.  Acme Oyster House, Commander's Palace Restaurant, Slice Pizzeria - St. Charles, Pho Tau Bay Restaurant, Cochon, Three Muses, Camellia Grill, K-Paul's Louisiana Kitchen, Juan's Flying Burrito, Antoine's Restaurant.  Hope that helps!

In NOLA I love Mandina's Restaurant and The Praline Connection as go to spots.

Coop's Place has amazing fried chicken that comes with rice and beans or, if your order it, rabbit jambalaya. It's between the Bourbon and Frenchman street areas.

I have tons of reviews and recommendations on my Nola trip in my blog post :)

http://coffeechalk.wordpress.com/2014/06/30/nola-trip/