I would save my points on this trip and low ball bid a 4* in the French Quarter on Priceline. I would start at $70 per night.
Just a guess, but it looks like you might get the Sheraton New Orleans Hotel over those dates. Just a guess. If you do Priceline make sure you specify 4*-5* and make it specific to the French Quarter.
Taxis from the airport are fixed price the the French Quarter. Don't miss Pat O's. Enjoy your trip! ^