All accommodations in Alamogordo are along White Sands Boulevard, the north-south highway through town, and parking is free.
Camping
I strongly recommend camping at White Sands National Monument.
If you'd rather have amenities, try Alamogordo Roadrunner (tel. 877/437-3003 or 575/437-3003; www.roadrunnercampground.com). It has laundry and grocery facilities as well as a recreation room/area, swimming pool, playground, shuffleboard, and planned group activities in winter. The campground is on 24th Street in Alamogordo, just east of the US 54/70/82 junction. If you're looking for something in between, Oliver Lee State Park, 15 miles southeast of Alamogordo via US 54 and Dog Canyon Road (tel. 575/437-8284), is a good choice, with 44 sites, 10 full hookups, picnic tables, grills, tenting availability, a playground, and hiking trails.