I just booked here: https://neworleansparking.com/reservation. There are several lots listed at that page, so choose carefully, some are covered, some are not, some are not for cruise passengers, etc. I booked the covered Fulton garage, 901 Convention Center Blvd.
Cost is $120.50, pay now, refundable less $5 up to 48 hours before your scheduled arrival time. They have a shuttle between the parking garage and the cruise terminal.
Doug