We have sailed out of this port many times.
The good things about it is that if you are driving in...parking is literally ON TOP of where you check in. So even if it is raining, you can unload, park and ride the elevator down to Level 2 to check in and never get wet. The rate is $14.00 a day for parking.
The not so good news is that if you are driving in, the hotels usually charge a parking fee that can run as high as $24.00 a day.
Of course, if you are flying in...none of this will be an issue. A Taxi will run you about $28.00 from the airport to the French Quarter district.
There you will find Holiday Inn, Hilton, Marriott etc to choose from.
We have stayed a the Holiday Inn on Royal and it was about a $10.00 taxi ride to the terminal the next morning.
New Orleans works hard to keep the tourist area as safe as possible, but still use common sense....especially at night. Stay on well traveled streets and well lit areas and "the more the merrier" doesn't hurt either.