Quite frankly, it can be cheaper (and more convenient) in the long run to park at the port. If you park at a hotel, you will need to take a cab to the port. Most cabs charge by the person so a family of 5 would cost close to $30+ to get to the port. Then another $30+ to get back.. Thats pretty close to the cost to park for 7 days any way. Also, the port has security and lots of activity which can help prevent any thing happening to your car. I have heard horror stories about leaving cars in Hotels (including people who work for the hotel getting paid to let others know what cars are ripe for ripping off). Then you also have the issue of loading and unloading your luggage a bunch more times. When you get off the cruise, you can go right to your car and you're off.
The last itme we were in NO, We stayed at the marriott on St Charles st. Its was beautiful and very reasonably priced. It was only 5 minutes from the port. I booked from Mariott.com
Just my Two Cents..