Monument Valley is in Arizona. Chaco Culture is the major National Park in NW NM. It's a fair drive over dirt roads to get to it. The road condition reportedly varies quite a bit. It was in good condition when we visited the park, but some times it can be a problem for passenger vehicles.
I was underwhelmed by the park itself, the Rangers we ran into were all in bad moods which probably affected my enjoyment of the park. It was just another Indian ruin and if you have stopped at a number of the same in Arizona, Utah and Colorado you won't see anything new.
There is another site that we didn't get to, Aztec Ruins. Just north of Bloomington. We stayed at a nice park in Bloomington but it was a bit hard to find. Desert Rose Resort.
The Cortez area has a lot more to do just over the border in Colorado: Mesa Verde, Canyon of the Ancients, Hovenweep, and of course the cannot be missed Moki Dugway. Lots of smaller sites like Goosenecks State Park and Canyon of the Gods and you can drive to Monument Valley from there.
