Try looking on the internet at the New Orleans cruise port. There is a lot of information on that site. If you are at all familiar with New Orleans you will see that the port is practically downtown. I looked at the site on the internet just quickly and it mentions the parking garages at the port being well lighted and patrolled.
Unless you get a big hotel with a big garage it is difficult for parking in N.O. And I heard from friends about finding their car broken into at the big Westin downtown and that was before Katrina. You might also look for a security number at the Port and check on security.
Or check on your cruiselines message boards on CruiseMates and ask the same question. That's where I usually go.