We drove from Disney World to New Orleans in Feb. (we actually live in Atlanta). It is a pretty easy drive. Don't know if you've been there, but New Orleans is a GREAT city so going a day early is a great way to start your cruise. Problem is finding hotels that aren't too expensive. To really enjoy it you need to be near the French Quarter where all the restaurants and bars are. Best to be within walking or taxi distance so if you drink a Hurricane at Pat O'Brien's you don't have to drive.
Another option is to stay short of New Orleans (we actually did that on our drive from Orlando as it was a 10 hr. drive). I think we actually stayed in Gulfport by the freeway. Short drive in, (about 75 miles).
Parking at the port is very confusing. Need to really follow the signs and traffic. It is one way in then out. After dropping bags, you'll go out and turn left and about immediately hit the lot. There is an elevator and bridge over the road. When you return we simply got a porter to take our bags to the parking lot.
If you're a fan of Cafe Du Monde, there is one in the mall attached to the port. So if you get there early Chicory coffee and beignets are a nice cruise beginning.
Boarding is a pain. Ours was delayed so everyone was in a single line. Since we were suite guests I asked an RCL employee for priority boarding (a suite amenity). He walked us to the front of the line, but if you are entitled to it and don't ask, you won't get it.
So plan to get there fairly early as parking, lines, etc. can take some time.
One "cool" thing is that it takes over 6 hours for the ship to get out of the Mississippi and into the Gulf. A very cool scenic ride. We sat on our balcony at midnight watching the lights on the shore (very close) and when we passed another cruise ship (coming in), they passed what seemed like around 100 yards apart.
Hope this helps. Have a great cruise.