Oh joy, something I can help with since I was BR native for 20 years
There are a handful of places in Baton Rouge you can stop for a smoke or two, but just so you know Louisiana state tobacco tax for cigars is 20% of the wholesale price, so our prices can be a dollar or two higher than MSRP.
Don Juan's Cigar Company has a location in BR, fairly close to the center of everything, very nice lounge area, a pretty varied selection (huge humidor). They're pretty much exactly what you would expect from a modern B&M establishment, but expect to pay a bit more for your smokes there.
Churchill's on Jefferson is a bar/liquor store/cigar shop. Tends to be where the money and "pretend money" hangs out at night. Nice place but since they're mostly a bar type place, the cigars are priced at bar prices (read: 2x MSRP). They are, however, the ONLY Davidoff White Label account in Baton Rouge that I know of. Selection leaves a lot to be asked for though.
Hemingway's on Jefferson is another hole in the wall type shop, but I don't know what's up with them. They've changed owners/managers like 4 times in as many years, and last time I was there the selection was nonexistent and the place was a dump. GRANTED, I haven't been there in about 2 years, and I hear the newest owner has renovated the lounge area, but I have no reason to go check it out unless I happen to be in town.
Also, there's a pub/grill style place called Fox & the Hound (chain place) that has food and drinks. They escaped the smoking ban by becoming a full on bar at night, but it's a mid to upper scale place that's cigar friendly and the food isn't bad at all during the day. Lots of good scotches and beers, prices are very reasonable. Just don't go at night or on a day that's a big sports/UFC day, the place is packed to the gills.
Now, here's the kicker. Can you escape about an hour's drive down I-10 to the *west*?
There's a great shop in Lafayette, The Cigar Merchant which (apropos any past employment I've had), is probably one of the best shops in the area. Full on lounge with all the amenities, private club area (day fee for non-members, but it can be waived), big screens, frequent domino or card games (poker in the afternoon in the club starting around 3-4), and more importantly a nice selection of smokes. The owner's a real nice guy, always willing to help people out.
Also, it's Lafayette, so there's only a dozen great places to eat in the city to great food, and there's a decent night life too. Personally, that's where I spend my lunch breaks and weekends
In NOLA, I personally like to stay at the Roosevelt New Orleans. It's a bit on the $$ side (I paid about $250 for a night a few months ago), but the Sazerac Bar is world-famous and the food is amazing. Plus, you're right near everything you could want to see or do.