Predicting the ideal time to book a New Orleans hotel for Mardi Gras is like trying to predict any other market in advance; it's only an educated guess at best. Some folks are booking already. If you can book now and it's fully refundable upon cancellation for at least a while, what's the harm in booking then keeping your eye out for a better deal? Based on my experience for MOST years, the best time to book will be around mid August. However, for MG 2011 the best time to book was late April 2010.
If you're preoccupied about having bathroom access, you probably won't have much problem. It's the folks who don't worry about it until the last minute that have the problems. If you think ahead a little bit, and do not mind purchasing food or drink, you shouldn't have much problem.
Like with most visits to New Orleans your hotel should be as close as economically practical to the activities you intend to pursue. If parade watching is the biggest part of what you intend to do, you should stay close to the parade route(s). I like watching parades on Tchoupitoulas between Poydras and Girod, but many parades, most notably Rex, Zulu and Endymion, don't pass by there. Quite frankly, it's hard to find a good place real close to the French Quarter or St. Charles Ave. to watch Endymion.
Although I enjoy the parades, I also enjoy the activity in the French Quarter, maybe even better. For me the ideal location would be Omni Royal Orleans, but I choose not to spend the money required for a room there during the last five nights before and ending with Fat Tuesday. JW Marriott is an overall very good location for Carnival; Renaissance Arts would be great for some parades, but is kind of out of the way otherwise.
Edited: 5:50 pm, April 10, 2012