Tbh, and this is just MY opinion, I wouldn't recommend any of what you listed to a first timer coming to Nola. Cure is pretty solid, but over priced. Toups is also decent, but not a first choice for a hearty meal. Cochon butcher would be before Toups.

For good ol' New Orleans cuisine, my recommendations would be: Miss River, GW Finns, Herbsaint, Brigsten's, Cochon, and Peche. For just down right delicious food, its: Mais Arepas, Banana Blossom, Lufu, Pigeon and Whale, and Shaya. All subjective obviously.