The amenity set above is the same that AaronJB posted in his original reply to this thread, so the guess would remain the Sheraton (although it would be cheaper to book thru the PRICELINE EXPRESS link he provided)
So why not the Sheraton, as it seems to fit the bill... just outside of the Quarter to avoid the noise, an easy walk to Bourbon at the start of the Quarter, as well as convenient to everything between Bourbon St and the river; not to mention well within your budget.
What is it that you're looking for that the Sheraton doesn't offer?
I do see this
4* Convention Center and Warehouse - Arts District (confirm your dates on the landing page) for $133
No Smoking Rooms/Facilities
==> my guess here would be The Old No. 77 Hotel which gets good reviews, but it's a longer walk to The Quarter and i'm not sure if worth $50+ per nite, but i mention in case it works for your needs
Please remember to return to BetterBidding and use the PRICELINE and HOTWIRE links on the board to begin your travel purchases... or thru our sister site MAPSandHOTELS.com for your regular rate purchases.