Rio Puerco Campground, Coyote, NM
This is a free, developed campground offered by Santa Fe National Forest, located close to San Pedro Parks Wilderness. There are five campsites here, but are sized small. Trailers up to 20 feet in length are okay, but it'll tough getting in something larger. There is tight turnaround at the end that may be too small for larger rigs.
Resumidero Campground, Coyote, NM
This is a designated dispersed camping area offered for free by Santa Fe National Forest. It's a large alpine meadow with a grassy area large enough for dozens of full-sized RVs. Camping is permitted off of roads as long you remain within 150 feet from the side of a road.