Scenic Off-Grid Glamping Camp with Private cook & Starry Night Dining near Lincoln National Forest, Alamogordo, New Mexico offers accommodations in Alamogordo, 23 miles from White Sands National Monument. Guests can benefit from a patio and an outdoor fireplace. Staff on site can arrange a shuttle service. The accommodation is non-smoking. The luxury tent has a picnic area where you can spend the day outdoors. El Paso International Airport is 75 miles away.