Fulton Place Parking garage is convenient.  You pre-pay for your parking reservation at: https://www.neworleansparking.com/ and then you show them your confirmation when you show up.  You can easily walk (about 2 blocks) to the cruise terminal or they have a shuttle.  If you use them, I suggest dropping off your party at the bottom level with the luggage before you park as the elevators are small and slow.  It's much easier for a single person to take the stairs down without luggage after parkin