Given the area described has piles of trash and little else to recommend it, it seems a shame to be close to gorgeous wilderness and stare at rubbish.
Head out just a bit further and turn onto the well maintained dirt Buckman road? There are canyons to explore and access to the Rio grande at the road's end, offering water in an area with next to none otherwise.
If these lowlands are too hot in the summer, drive up Artist Road to Big Tesuque or the ski-way at the end of the road, where shade, cold streams, and elevation keep nights pleasant even in July or August.
You won't be any further from Santa Fe, although it can take awhile to drive from the river or ski-way to town if you park as far away as possible.
All of the above sites have fire rings and vault toilets, and Big Tesuque and the ski-way have some sites with picnic tables as well. Firewood can be scavenged, especially if one gets away from the immediate campsite area.