From the NPS site:
Directions
Hovenweep National Monument is located along the border between southeast Utah and southwest Colorado, just north and west of Cortez, Colorado.
By Car
Paved roads lead to the visitor center and Square Tower Group from Cortez, Colorado (County Road G / McElmo Canyon Road), from Highway 191 south of Blanding, Utah, and from Pleasant View, Colorado. All roads into the outlying units are dirt and are not maintained regularly, making them impassable during inclement weather. High-clearance vehicles are recommended for visiting these sites.
Using GPS to find your way to Hovenweep is not recommended. Since Hovenweep has 6 different units with numerous paved and dirt roads intesecting each other, GPS will send visitors to unknown locations other than to the park. Using a map is recommended.
MAPS