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.
The River Parishes (St. Charles, St. John, St. James) are pretty much their own region too. It's a mixture of New Orleans and Cajun plus a healthy dose of German.
What about drive-through daiquiris? Seriously, my most missed part of Louisiana. If we weren't up for cocktails, my wife and I would each get a sonic cup sized frozen daquiri of pure deliciousness. For whatever reason this is just not a thing in most states.
Lafayette, Baton Rouge, New Orleans are all great. The middle of the state (Alexandria region called Cenla for Central Louisiana) is a mixture of south Louisiana influence and the more Northern influences, so the Cajun influences are there, but watered down. Northern Louisiana is nothing like the rest of the state. With the exception of Shreveport and Monroe (maybe Ruston) it is mostly small towns and has a very Bible belt feel to it. Some call it "South Arkansas" as it has more in common with that region.
I've had gumbo and jambalaya made by Cajun family and the best places in the South and it's much better than anywhere else in the US when it is made properly. I've had plenty of what's called gumbo/jambalaya in other southern states and it is good, but doesn't quite taste right.