Three downtown offices, as their own pages describe them; the first two sit within about half a mile of the terminals.
No company returns cars at either cruise terminal that we could find, and the Port of New Orleans’ cruise pages talk about parking, directions and terminals without a mention of rentals.
That makes the Hilton Riverside counter, at the foot of Poydras Street, the closest you’ll get. You reach it through the Outlet Collection at Riverwalk, and its own listing ties it to the ships — Budget writes “services Cruise Ship Port” beside the address, and Avis calls it “New Orleans Hilton Cruise Ship.”
It still isn’t a shuttle desk — nobody there says it will drive you. From the lobby it’s a short cab, and the city sets that fare at $14 for a single rider, $8 per rider once there are two or more, or the meter if it reads higher.
Other downtown options start with a second Avis and Budget counter at 1317 Canal St (8 to 6 on weekdays, 8 to 2 Saturday, 8 to 1 Sunday). Sixt works out of the Hyatt Regency at 601 Loyola Ave (9 to 5 weekdays, 9 to 1 weekends), and Enterprise has a branch at 1019 Baronne St as well as Canal. National and Alamo rent only at the airport.
Avis and Budget will collect you downtown with 24 hours’ notice, and both Enterprise branches list “Pick-Up Service Available” — that’s for starting a rental, not for a ride to the ship.