I highly recommend Rhonda's Rental on Algiers Point. Not only is it a great location, but the home is charming and the neighborhood has great little restaurants and a coffee shop (keep in mind dining ends before it gets too late). Definitely check out their binder of helpful info and be sure to explore the neighborhood one of your first days (some spots closed on Mondays). The transit app offers a great multi-day pass for the ferry, trolley, et all.
I would definitely rent the home again and will certainly recommend it to friends and family!