I just love New Orleans! My wife and I would love to rent a house there for a few months a year once the kids are grown.
Gumbo - I'll walk around and pop in nearly every place to try a cup of gumbo, they're all so good! My favorites, K-Paul's and Chartres House Cafe.
Beignets -Cafe Beignets inside Legends Park. Some nice music, drinks and some beignets with a nice delicate center (same mix as everywhere else, just not overcooked)
Breakfast - in the quarter I liked Oceana's. Outside of the quarter...Elizabeths Restaurant (loved this place)
August is nice, as is Domenica...Cochon was heavenly (ask for the chefs table with a view of the kitchen)...Commanders was okay.
If you go to Pat O'brien's you may want to turn the glassware in to get your deposit back.
Be sure to go to M.S.Rau Antiques on Royal St., this place is a hidden gem...hidden in plain site.
Take a cab to The Joint, it's a small little wonderful bbq place. Great Bbq, I'd recommend the sampler and a side of their chaurice sausage.
For music, you can go around the quarter for an enjoyable night of music. When you're ready, head to Frenchmen Street. This is where all the musicians went, filled with great music...and plenty of locals. You'll also find some nice places to eat around there...this is really a great street for music and food!
If you take the trolley you can head to Magazine street and walk around the Antique shops and small taverns. We also just loved the live oaks in Audubon park...another must eat at is Sucre, sooooo good!
I could go on and on ;)
Have a great time!