The Navajo people have always had a tradition of being hospitable when having visitors. It is a custom to always make a warm inviting meal for visitors. To share a local side dish such as fry bread. This is still true to this day. There are many locals in the area that have continued with these traditions and offer Airbnb's and VRBOs. Check out the wonderful Airbnb's here.
Goulding's Lodge is a great hotel that has a very unique history and position in Monument Valley. They have campgrounds cabins, and hotel rooms that are for everyone and their needs.
The View Hotel has some of the best views out of any of the hotels. It sits an the edge of the tribal park and above the most iconic buttes. They have a campground, cabins, and hotel rooms available for booking.