There are plenty of nice spots to camp along North Star Road, north of Mimbres, NM. You'll find dispersed campsites with fire-rings all along the edges of the road and on spur forest roads sprouting from it. North Star Road is usually well maintained and most vehicles should make it to at least North Star Mesa.

Nothing in terms of services and amenities, but nice hiking nearby. Very clear skies at night. 

As always, please follow LNT principles when dispersed camping.