About 20 miles from Monument Valley is Kayenta, a small town that has a number of motels including the usual Best Weston etc. You should find a room at a sensible price there. There is only one hotel near the valley and I believe it is quite expensive and usually busy.
Have a good trip and may the light be good for you.
Just got back from that area. Definately stay in Kayenta. You will see several motels that are not full right on the main hwy. There is also a good little resturant that looks like a huge blue wooden hogan that has fair Navajo tacos. Just remember to obey the speed limits near the towns and the monument. Also if you go off on a side road, make sure that you ask permission if a house is near. 4 years ago i went off on one, and stopped near a house, stayed on the road, but the man in the house came out waving a large stick and running at us. I left fast. this time I had my foster daughter along and she translated for me.