Located just an hour from Monument Valley you will find the Valley of the Gods. There are two things that make this spot interesting. First it has similar rock and land formations and second it is free! (I could say that it is also less crowded).
The route is self-guided and a great place to photograph at your own pace. There are plenty of spots to pull off the road for a picnic lunch (or just to admire the view) and you don't feel rushed or crowded.