Happy's recs are spot on, and I bumped my N'awlins vacation thread from last month for you. Also good are The Gumbo Shop, Magazine Po-boy, Mahony's (more po-boys... get the Peacemaker), and K-Paul's, which serves lunch a few days a week. Domilise's is great, and some on this site extol the virtues of Parkway, but I've not been there yet.
Mother's on Poydras serves a little of everything Cajun, Creole, and Soul. The bread pudding is divine but not for diabetics. You must eat there at least once. Acme is good enough, but it's touristy, so don't go.