Okay, Joe, my wife and I went over to NOUPT yesterday and did a little research, as we are in New Orleans this week.
First, you don't even have a choice to stay overnight in the depot. It's closed from 11:00 PM until 5:30 AM. The neighborhood is not safe after dark. You'll need to book a hotel for the night. There's a Hyatt not too far from the depot (no, don't walk to it at night) and there are good hotels downtown on Canal Street (Marriott, Westin, Hilton, etc). You can stay farther away for less, but the longer taxi ride eats up money, too.
The station is in good condition, and has a lot of molded plastic chairs in the waiting room. There is the Magnolia Room Lounge for first class passengers, but, the Sunset leaves in the morning, so you'll have to get there very early if you want to use the Magnolia Room.
The seashell ballast is now buried deep under a lot of large granite ballast. Environmentalists stopped the salvaging of seashells for gravel.
The Rampart Street streetcar goes right to the station, but is not a 24-hour operation. Also, luggage does not do well on New Orleans streetcars. Taxi or Uber or Lyft is the answer. I suggest taxi, as I would not want to wait for Uber or Lyft after dark there.