The Maison Orleans is pricey but fabulous. It's one of the Ritz's boutique hotels, and is connected to the New Orleans Ritz but also has it's own very private street entrance about 1 block from Bourbon street.
I stayed there last summer while in town for a convention (the Ritz owed me an upgrade), Lenny Kravitz was on the same floor 2 doors down.
http://www.maisonorleans.com/