Re: Monument Valley?
Your on the Navajo Nation there so your best bet is to pay the fee and stay in their campground.
Not too far to the north is Cedar Mesa and Muley Point. There's dispersed camping as well as outstanding views with Monument Valley some 40 miles distant to the south and the goosenecks of the San Juan below.
Near Mexican Hat you can drive down to the San Juan and camp right along the river.
2005 E350 RB 6.0 PSD for extended fun
1989 Landcruiser FJ62 for local fun
2011 VW TDI Golf for hwy fun