This area has five to ten campsites suitable for small rigs (we pull a 17-ft trailer, wouldn't go much past 20ft).   From the almost-ghost town of Bowie, AZ, take the Apache Pass Rd until you reach the Happy Camp Rd.  This is a good gravel/dirt road that goes up to a public picnic area (no camping).  Here take the turn-off to the right to continue on Happy Camp Road.  Soon you will see turn-offs and side roads.  We didn't explore the side roads but we did see a couple of small rigs a hundred yards or more from the road, so it is possible to find sites there.  As you continue along the road it gets worse and you'll need decent clearance (there are also sites before the road gets a little dicey, closer to the picnic area.  About a mile from the picnic area we backed into a site right below the rocks with a grand view of the plains below.  We camped for two nights, saw no-one.  In late September, 90s during the day and 60s at night.

This site is on the *other* side of the hills from the Chiricahua Monument.  To get to the monument, you can either go back to Bowie, and then to Willcox, and back to the Chiricahuas, or you can take the Apache Pass Road (the one you turned off from to get to the campsite) over the hills, past the ruins of Fort Bowie (you will have to hike 1.5 miles to the actual ruins).   Total time is probably the same either way.

We drove past the campgrounds near Portal AZ as we were exploring.  In late September, they were all full and there were lots of ATVs buzzing around.  Compare and contrast to our empty, quiet campground with neat-looking rocks and a fine view. 

We had two bars of Verizon coverage and it was fast.