These are all in the French Quarter, but I've been to all of them and they'd definitely be worth a cab ride!
Fine Cigars: Mayan Import Company: Welcome to your Big Easy Tobacconist (Exchange Place....I haven't been to the other location)
Cigar Factory New Orleans - For one of the best cigars you'll ever smoke!
Don Leoncio Cigars
Crescent City Cigar Shop - New Orleans, LA.