My favorite is La Quinta on Williams Blvd.
It is relatively new, quiet and safe. They have the usual breakfast buffet,
and a free shuttle to the airport in case you are spending a post cruise night there. If you are driving to N.O. you can leave your car there for free if you spend the night before. It is not in an enclosed area but the front parking lot is monitored by closed circuit TV. I've never had a problem, but that's no guarantee.