There are three places to stay on the atoll for visitors. One is the small but luxurious Embankment Hotel which is near the center of New Tortuga. The other, more natural and primitive in its environment, but no less luxurious, are the beach huts that make up the Lost Island Resort near the breaking surf. In the huts, you can fall asleep to island breezes flowing through nearby palms, or soothe those surfing muscles in the private hot tub and fire pit.
You can also stay at the Galactic Hotel in the Orbital base station.