For a 7 day cruise, its $84.00. ($12.00 per day) Try to get there around 11.00 am or 11.30 . We're only 3 hrs away from New Orleans, so no overnight stay is needed. This has always worked well for us. Get there any earlier, and you'll have to wait.
There are Motels there next to the Terminal that you can leave your car, if you spend the night there before you cruise. All you need is to show your cruise documents too prove your cruising. I'm not sure on the names of these hotels, maybe someone can help you with that.
Try this website= www.nola.com
If you need a hotel try the Maison St. Charles. Their cruise package is $89 per night and they give free limo rides to the cruise terminal on cruise day. The parking i think is $5 per night with the first night being around $13 --so i've heard--we'e flying so don't need the parking but this is where we're staying in Aug. BigJohn stayed there for his cruise and he said it was really nice.