Photos can not do Moki Dugway justice. Probably that's why so many people posted movies on youtube from their drive on this very special road. It is a series of sharp switchbacks that descend 1100 feet (350 meters) on a steep gravel road over less than three miles (5 km).
As we were coming from south (heading from Monument Valley to Natural Bridges SP), we were driving up the switchbacks, which was a heart-stopping experience. The engine of our car was making excessive noises all the way up, and we were in doubt if our car will make it to the top without falling down... But I can imagine that driving down must seem even more scary. Then you probably worry if your breaks will not burn... Either way, it is a great experience to drive there and views from the top are simply stunning. So I highly recommend including this road in your itinerary if you are traveling anywhere nearby it.
Beginning of the road (or the end, actually, in our case):
View from the top of Cedar Mesa:
Notice the road on the right side of the photo. We drove on this road just before we started driving up the switchbacks to the top of the mesa:
Valley of the Gods: