I will add a couple spots.
Toast is a great breakfast spot by Fairgrounds. Elizabeth's is great for brunch which I see is added. eat at elizabeth's and then walk down to the quarter from there, you can go over the bridge and walk through the park along the river, you will need the walk after eating there.
I like the PO Boy's at Parkview Bakery. ( surf and turf Po Boy) Rosedale is very good as well, sit at the bar.
Two Best restaurants that I have been to there recently are Compere Lapin and Shaya. Lapin is great for brunch or dinner. Shaya is middle eastern type food but well worth it. ( different for NOLA) You will need a res at Shaya 2-3 weeks in advance unless you want to eat super late or early
Classic New Orleans type is Jaquimos ( SP?), no reservations so be prepared to drink at the dive bar next door. Maple Leaf
Turkey and the Wolf is a bit odd but great for lunch
Best spot for Music I Like Frenchman Street ( DBA or Spotted Cat)
Best dive bar with cocktails: Bar Tonique. No food but great drinks
Best Gumbo at a dive type restaurant, Liuzza's by the track.
And yes I have spent a lot of time in the great city of New Orleans and haven't set foot on Bourbon Street in probably 10 years. I wouldn't even bother, not worth it and too much other great stuff to do. Definitely wouldn't recommend it at night. Nothing good will ever happen