I'm not from LA but live in Birmingham, so I can tell you about some of the restaruants I've been to.
Home Restaurant:
Lyle Broussard L’auberge Casino & Resort (Lake Charles) - Avo & Dram
Ryan Andre Le Creole (Baton Rouge) Bistro 218
Cory Bahr Cotton (Monroe) Highlands Bar & Grill/Bottega
Manny Augello Bread & Circus Provisions (Lafayette) Little Savannah
Michael Farrell Dickie Brennan & Company (New Orleans) The Club
Keith & Nealy Frentz Lola Restaurant (St. Tammany) Ollie Irene
Stephen Naegle Spirits Food & Friends (Alexandria) Dixie Fish Co

I haven't been to Avo & Dram, Little Savannah, The Club, Ollie Irene, or Dixie Fish. I have good friends and coworkers that have been to The Club and Dixie Fish though. Dixie Fish is in the old Bahama Breeze location on 280. They serve only Alabama seafood, and have several, maybe all, of the local breweries selections. Big patio with a big screen TV and they do good business during games. The food is great, from what they've told me.

The Club is a private club near downtown, and it is kind of old school country club. At least it was a few years ago when a coworker of mine at the time was out theredoing thier audit. He said they ate there some days and the food was great.

Bistro 218 is in downtown on 20th street on the northside. My dad and I have had their lunch a few times. They have pretty good gumbo, and I've had their steaks, some seafood, and a few other things. Good desserts too, and I usually get the creme brulee. Last time we went, Dad said we really should bring the wives for dinner there one night. It is in an older building on the ground floor, but has a loft appearance and there are some tables up on a catwalk near the back. There is a long booth bench along the left side and small tables with one chair on the other side. Lots of exposed brick and is a neat place.

I haven't been to Highlands or Bottega in years, but it is one of the nicest restaurants in town. My parents took me and my wife there a couple of times. White tablecloths and servers in suits/tuxedos, at least on weekend nights when we went. About what you would expect for the price you pay. Very good food, big wine selection, and they're generous with drinks from the bar.