@Xochitl First things first: po'boys. Killer Po'boys is great, and certainly worth going to (either at their original location inside Erin Rose Bar, or their new stand-alone location), BUT these are far from your traditional po'boys. For classic, NOLA tradition, go to Parkway or Domilise instead.
In re: the must list: Make sure you wait until they bring out a fresh tray of fried chicken at Dookie Chase -- it's excellent (love Miss Leah!), but you really want to get it when they first bring it out. Haven't been to Angeline, so I cannot comment. FWIW, we usually do Commander's for a weekday lunch -- Monday thru Friday, they have 25¢ Martinis at lunch. Personally, NOLA's "thing" for having a Sunday Jazz Brunch has never been a great draw for me. And in addition to Cochon (where we usually have lunch, but dinner is also wonderful), don't forget Butcher (née Cochon Butcher) next door: great sandwiches and charcuterie -- grab some and go have a picnic along the Mississippi or in one of the great parks in the city . . .
re: the Undecided list -- I agree about Brigtsen's, in that I had a great meal there years ago, haven't been back in many a year, and also haven't heard much about it lately from any of my friends. Wasn't impressed by La Petite Grocery the last time I went. Compere Lapin is on our list, but something else came up on our last two visits, so we still haven't made it there. I would definitely plan on Patois (mentioned above) and Clancy's located way the heck Uptown (and which I really should have included in my listing above) . . .
@TheCookie @President_Mochi @Xochitl Toups' Meatery (it's T-o-u-p-s-apostrophe; chef's name is Isaac Toups). Very casual atmosphere, a few outside tables. Very nice wine list -- both bottle and BTG. Great food -- again, lunch (this past April) -- really enjoyed it, and will definitely go again.
@Xochitl, just to give you an idea (which really means "feel free to completely ignore this"), this was what we did on our last visit (April 2016):
Dinners: Restaurant Patois,, Sac-a-Lait, R'evolution, Shaya, Doris Metropolitan.
Lunch: Killer Po'Boys, Galatoire's (Friday lunch), The Joint, Brown Butter Southern Kitchen (Sunday brunch -- no jazz, but GREAT food!), Cochon -- and sandwiches from Butcher for the flight home.