One of those places is called Bloody Basin, in the Tonto National Forest. I don't know if its called Bloody Basin because the Indian wars that were fought here, or the red tinged soil, but it is a really cool place to explore. One could probably spend a lifetime exploring here. But the catch is that water is really scarce.
We decided on an off trail excursion. Doesn't look too bad from this view, but let me tell you, when you get down there a midst all those prickly plants, it can be poke city. There is a bush of some kind that grows here that had barbed hooks on it which embed in your clothes and skin when you get too close.
As remote as this place is, the roads back here are remarkably well maintained. But even with the nice roads, we only saw perhaps 5 other people all day.
That peak in the center is called Turret Peak. In 1873, US Army scouts sneaked up on some Apaches that were hiding there, killed 57 of them, and captured the rest. The ambush basically broke the back of the Apache resistance. I love how rich in history Arizona is, despite how sad it can be. It really adds a new dimension to my outdoor experiences.