Mystery Valley is a section of Monument Valley that is only accessible by visitors who have a Navajo guide. This is probably for the best because there are several sensitive archeological sites, several Navajo families whose homes are in the area and do not want to be disturbed, and perhaps most importantly, the roads are very poor with deep sand and no signage at all. It would be very easy to get lost here. Though there are a few tour providers for Mystery Valley, it is not that popular with tourists because it requires walking and a bit of rock scrambling to get to the best sights. It is likely you won't encounter other visitors on your tour of Mystery Valley.
Aside from solitude, Mystery Valley holds a large number of very well preserved Anasazi (Navajo for "the Ancient Ones") ruins and artifacts, plus it has stunning scenery and views of Monument Valley in the distance. The Navajo arrived in the Four Corners area about 500 years ago, hundreds of years after the Anasazi had abandoned their cliff dwellings and moved south. Navajo people do not have a lot of reverence for the abandoned pueblos, but rather regard them with a bit of superstition. The tours of Mystery Valley generally include a lot of context about the Navajo way of looking at the world and their way of life. The guides on these tours tend to be older and more willing to discuss their personal stories than the average Monument Valley tour.
Allow between three and four hours for this tour. It is worth scheduling it as a sunset tour, because the views of Monument Valley from here at sunset can be amazing.