Red Stick Farmers Market is a producer-only market in downtown Baton Rouge, with local growers and food makers selling seasonal produce, baked goods, prepared foods, and Louisiana pantry staples. It has been one of the city's better places to see everyday food culture rather than a staged tourist version of it.
Go in the morning, when the stalls are fullest and the weather is easier. It fits naturally with a walk between the state capitol area, downtown museums, and the riverfront.