My wife and I were on a journeys cruise on Glory this past December out of New Orleans. We stayed at the Hampton Inn & Suites New Orleans Convention Center, 1201 Convention Center Blvd., New Orleans, LA (1-888-861-8331).
They have a Park and Cruise package and the parking is in a covered garage attached to the hotel. Don't remember the fee but it is discounted from the normal fee and is less expensive than port parking. Also, there is no limit on the length of stay. When you get to the hotel you just need to tell the concierge you have the park and cruise package. There is a free shuttle to and from the port. You need to sign up at the front desk for the shuttle when you check in. We wound up taking a taxi back from the port, at the end of the cruise, because debarkation was such a mess and didn't want to wait for the shuttle. We enjoyed the hotel. Got an upgrade to a suite because our room wasn't ready, even though I was about 4 hours early.