Lafayette is indeed the heart of Cajun Country (Acadiana). Although it spills over in various degrees to other parts of the state, Acadiana itself is a well-defined, specific area that includes Lafayette, Carencro, Breaux Bridge, St. Martinville, New Iberia, Abbeville, and Crowley (this list is not exclusive, but just to give the idea).

Baton Rouge and New Orleans are most definitely not Cajun. Sure, you'll find pockets of authenticity, but generally speaking they're not. New Orleans is Creole, a mixture of various influences but primarily French, Spanish, and Native American. There are other parts of the state that have a fairly pure French heritage that are not Cajun nor Creole (towns in the central part of the state like New Roads and Ville Platte).

'Cajun' is the one that is most well known, but Creole and non-Acadian French (ancestors came directly from France, not exiled from Nova Scotia) also have outstanding cuisine. Some of this may feel like splitting hairs, but the distinctions are important for some of the Louisiana natives.