The normal lot for that is the whale lot which is a wide open surface lot right by the river walk mall. I would recommend Fulton Parking Garage instead. Security is going to be better and they have a free shuttle to/from the port. The absolute cheapest cruise parking is their rooftop parking. But indoor isn’t that much more. Make sure you switch the drop down from hotel to cruise parking and you’ll see the indoor and rooftop options.
https://www.neworleansparking.com
What you may want to consider is booking Hilton Garden inn as well. Book one day of hotel parking for that. Then book your cruise parking. HGI is right by Fulton. Park, walk across the street to your hotel, Then walk back across the street the next morning to take your shuttle to the port.
I did that before my Glory cruise in 2019. What I did was just bring enough stuff for the night over to the hotel. Then when I came back in the morning I dropped my dirty clothes in the car and grabbed my suitcase for the cruise. Took the elevator downstairs and got on the shuttle.
https://www.saintgregtravel.com/new-orleans-hotel-review-hilton-garden-inn-convention-center/