Yesterday's mystery place was Muley Point, at the edge of Cedar Mesa, overlooking the meandering San Juan River gorge, with bits of Monument Valley in the distance. And dispersed camping. Sounds good. Sounds like it might worth the drive up the notorious Moki Dugway.
I had driven up Moki Dugway once before. It was a slightly anxious experience, but this time it was no big deal. The fact there was a lot of oncoming traffic the first time (including a huge beer truck) but none yesterday probably had something to do with my relaxed attitude. Driving down might be a different experience.
The road to Muley Point is supposedly impassible when wet. When dry (like yesterday) there's a one-to-three inch layer of orange dust/powder/sand until the road crosses into the Glen Canyon National Recreation Area. Then it's gravely. And white.
Before the actual point, there was a turnoff on the left. A mostly solid rock surface with evidence someone had camped there before. I checked it out.