When we stopped for a quick meal in Kayenta at the local Burger King, we were pleasantly surprised to discover that it also held a small museum chronicling the history of the role of the Navajo Code Talkers in World War II. It was quite fascinating. The Burger King is owned by the son of King Mike, one of the Code Talkers, and he had access to lots of materials about them. I learned a lot about a subject I knew little about before from this exhibit; if you're looking for a casual meal or a snack when passing through Kayenta it's worth a short stop to see.
When you get to Monument Valley, you can drive as far as the visitor's center on your own (there is a fee for driving off of the highway onto the reservation), but to go deeper into the Valley you have to go with a tour from a Navajo guide. I do recommend it, you get lots of interesting information, and you can't really see the most awesome formations from the paved roads. We stayed at Gouldings and went on their tour, which was great, but there are a number of guides soliciting business at the visitor's center, so you can take your pick.
I second Bob Brown's recommendation of a side trip to Goosenecks State Park (north of Monument Valley), it's an amazing sight, and not too far out of the way.

History and burgers - my kind of place!

Thanks everyone for your help, much appreciated.

Actually, the Navajo did have a good bit of say in their choice of land. They wanted the land of of their ancestors - of course when their ancestors settled there, it had lots of tall grass (which couldn't recover from over-grazing).

They have kept much of the land within their four boundary mountains.

Wasn't it the Hopi that determined their own land? Basically where the blue corn would grow. I believe much of their land was given over to the Navajo during the land reforms in the latter half of the 20th century.

Tony, I am pleased to report that you will be perfectly safe in the Monument Valley and in areas populated by Native Americans even though you are Caucasion.

Hope this helps.