Tim and Susan,
We stayed in that free campground there in Chinle called
Cottonwood Campground. This campground in our opinion is nothing to write home about, but it was very convenient for the 3 days we stayed there. This is a poor indian community, so be prepared to share the state park bathroom and the water spigots in the campground. We felt safe there, though.
Spider rock campground is also listed, but it is up a muddy road, and not someplace I would care to stay. Make sure you take the short hike up to Spider Rock!!!
Monument Valley is nice, but we think Valley of the Gods k(near Mexican Hat) is more spectacular, and there is no entrance fee. You can stay at the Goosenecks SP for free too...boondocking. There is also a RV Park in Mexican Hat...real primitive, but doable.
From Goosenecks SP, you want to see Moki Dugway and Moki Point, Valley of the Gods, Monument Valley, and Natural Bridges National Park. You could also stay in Blanding,.....we used that place to clean out our tanks.
If you need more information for that area, give me a call, would be happy to help....can even send you coordinates!