After getting to 12,633' on Humphreys Peak, I descended about 20' below the Earth's surface in the nearby Lava River Cave. As you can see from the photos, I really planned all of this out, bringing in several Klieg lights and a laser effects machine. It took a long time to bring them down into the lava tube, but then I couldn't find the outlet. So, you get what you get.
As with Humphreys Peak, the cave was beset with tourists. I only went partway because I'd heard that there was a large group at the end. It also didn't seem to be worth the walk. I was also worried about the impact all those people have on bats. Per the info board from the Forest Service, bats at least visit the cave. Some of the many visitors might tramp in the spores that cause White Nose Syndrome; that syndrome has killed millions of bats in the USA. Yet, there was no ranger around nor was there a station to wash your boots in hydrogen peroxide. I don't know why the FS is seemingly so sanguine about this; maybe they've just given up.
Afterwards, I drove down a good dirt road (171) to the 40 and along the way I saw why there were so many tourists: that section of the Coconino Forest was full of dispersed camping from large RVs to tents. It looks like a good place to camp and it's large enough you can probably find some solitude.