First, a few questions to clarify suggestions better, please:
Budget in US$, and does that include wine/Lcohol?
Style - ultra-casual to fine-dining?
Cuisine - Creole, Cajun, Seafood?
Allergies, or aversions?
Those will give folk a start.
Best of luck,
My suggestion is to research Happy Hours as well, for instance the Blind Pelican has 25 cent oysters from 4 to 8 pm daily...
August is "Coolinary" when restaurants offer fixed price lunch and dinners for a very reasonable price.
Deanies seafood and Mothers
For cheap but good, cajun Mikes which we go to for burgers every time and willies chicken shack.
Was cajun Mikes also known as Lorenzos?
Willie Mae's Scotch House and Domilise's both serve great food. Both are casual and inexpensive. Be prepared for waits at both. Go early.
Super Expensive differs from each person. I think Acme's is mid range if you are getting oysters. If you want cheap consider places like Johnny's Po-Boy even though not cheap but you don't have to worry about a server.
Keep an eye on this link to find menus for Coolinary 2018. Probably won't begin posting until mid to late July. Restaurant Week takes place in early September as well. You'll be able to find menu at this site beginning in August.