You don't have to go all the way to New Orleans to get some good food while in Baton Rouge. For lunch, I would not miss The Silver Spoon on Jefferson Highway. Excellent crawfish soup and almond chicken salads. It is a bit on the "society ladies of leisure" side but worth it. Dearman's, in the same strip mall, has some of the best cheeseburgers and fries in the state of Louisiana. It has virtually NO atmosphere but for the people watching. Maxwell's Deli for excellent sandwiches and lunch specials. George's, a bar under the interstate on Perkin's, is a dark, smokey lounge with excellent po-boys and fries.
For dinner, try Mansours on Corporate ave. with traditional Louisiana food, Tsunami downtown for innovative sushi, Juban's for creole food in Perkins, Fleur de lis for this crazy square shaped pizza, and Phil's oyster bar for, well, it goes without saying.
I'm biased, since I live in NOLA, but I think EVERYONE should come to New Orleans and take the disaster tour. You won't believe it - and while you're here, have a meal at Galatoire's, 7 on Fulton, Jacques-Imo's, the Palace Cafe, Vizard's on the Avenue, Cafe Adelaide, or any of our wonderful restaurants. It's definitely worth going out of your way by 80 miles!
Good recs so far. I'd add a few:
Mandina's - a New Orleans resto that opened here after The Thing. Good "neighborhood" style New Orleans style seafood and italian.
Brandt's Maisonette - fine dining in a small, intimate setting.
Second that rec on The Chimes (casual near LSU) and Mansur's (fine dining on Corporate) - both great.
Any specific types of food you're looking for? Lot's of Asian and Middle Eastern choices and a great Indian place too ("India's" on Essen Lane).
jubans is pretty good and so is mansurs. i'd stay away from mike andersons though, I prefer phil's oyster bar. Cafe Asia is top notch vietnamese, Rama is pretty good thai. The black forest downtown is good for german. The Chimes has good regional fare. If that is what you are looking for check them out and go buy Phil's their seafood is great