There are 2 parking areas in N.O.
One is on-site at the dock and it is secure but not covered.
The other site is a parking garage several blocks away. It is entirely covered and shuttle service is provided every 15 or 20 minutes.
I've not sailed from NOLA for about a year but at last sailing cost was $8/day for either facility.
Some TAs sell parking vouchers in advance and some of the NO agencies will give you a free voucher if you book an outside cabin with them.
The drill goes like this: drive to the port, easy to get to - take the Tchoupitoulas exit from the expressway and follow the signs, they're well marked if you look for them. Drop off baggage in the circular drive and then go park the car in the on-site lot. If it's full they will direct you to the garage. Take the shuttle back and get in line for check-in.
After check-in, wander up to the Riverwalk, which is a big shopping and food court and soak up some jazz, get some cajun cooking and a bloody Mary while you ogle your ship.
There is a nice deck that extends the entire length of the Riverwalk where you can sit outside and watch the boat traffic on the Mississippi. Nice way to spend an afternoon - unless of course it's June, July, August, September . . . uh, on second thought - enjoy the view from inside unless it's Spring (that's 4 days in February).
New Orleans is a fun port but maybe I'm biased since I'm from there.