Run, Forrest, Run!!!
Monument Valley - on the border of Arizona and Utah in Navajo Country is some of the most amazing buttes, mesas, columns and spires in WORLD, let alone Arizona. There are paths leading through and in between the formations such as the 'mittens'; but it is almost all unpaved roads and on the Navajo Reservation, so expect to pay the locals some dough for the priviledge of trodding on their sacred grounds.
Don't even dream of taking pictures of an actual Navajo Indian - photographs are considered evil to these people (unless you slip them some cash first, of course). There are stories of some Navajos walking in front of tourist's cameras then demanding payment for their 'services'.
Now, I respect 'the people' enough to not take their picture. I learned this after trying to take a picture of a VERY old (looked at least 105 years old) Navajo woman years ago. I tried to talk with her as she was very interesting to me and probably had many stories to tell, but she didn't talk to me. She saw me with the camera and shied away, so I attempted to 'steal' a picture of her when she wasn't looking. Well, I took 8 pictures or so of her and she hid her face EVERY time, then when I was out of film she gave me this look like she was cursing me with every ounce of her being, I was bugged out all day waiting for ill deeds to happen to me... nothing happened, but I still feel bad for harassing the old lady...obviously!
If you do visit Monument Valley and have a little extra time, wander up a bit into Utah and see Valley of the gods. It's a few miles past Mexican Hat, on a dirt road with SPECTACULAR views, you might see 2-3 other cars on the entire trail and best of all, free!!!