Campsites are close but not as close as many of campgrounds that charge fees
To get to this great location go north past White Sands National Monument on Highway 70 to mile marker 203. Look for the sign with the binoculars and the number 61. Turn left. Watch for traffic coming south on 70 and when clear then cross the highway and proceed slowly between the two fence post. There are several camping spots to choose from.
Coordinates are 32.811124 -106.12017
a video of the drive into the BLM camping area