We camped here on a Monday night in late September and had no trouble finding an open site without a reservation. The spots were a little close together, but thick foliage in between provided some nice shade and privacy. There was also a nice stone wall at our site to help with erosion control. Good fire pit too.
Toilets were clean and stocked.
The Black Canyon Loop trail at the north end of the campground is a great jaunt up to a view of the Santa Fe watershed and the Pecos Wilderness. It's 1.3 miles long and does a lollipop loop allowing for different views on the way up and back - would highly recommend.
This is a decent Forest Service Campground on Hyde Park Rd. (NM475) near Hyde Memorial State Park. It is a pretty spot (nice trees/shade) and is conveniently reached from Old Santa Fe (which means it can be pretty slammed). There are a few walk-in sites and many more drive-in sites. Get there early so you can grab a spot far from the toilets (smelly!).
This site has a limited parking. There are about 8 sites and it fills up really fast. The host was a little rude but still helped us. The sites were on the medium side if it was on a 1 to 3 scale. You do have to reserve a site and there are concrete slabs on the campground so you have to find vegetation on the side to put your tent on.