The two that come to mind are Mansur's on the Boulevard and Juban's. They've both been around for a long time and consistently offer some of the best French/Creole food in the city. Enjoy your visit to Baton Rouge!
Agree with the suggestions of Mansur's and Juban's (my preference). Depending on how long you will be in BR, you might want to also consider Galatoire's Bistro...granddaughter of the New Orleans Grande Dame.