Hovenweep National Monument is a bit out of the way but one of the places I had on my list to see someday. After getting down the road a bit and getting off the beaten track, you'll arrive at the site that is just 25 miles straight north of the four corners (as the crow flies), where CO, UT, AZ and NM meet, but it takes a good map and some understood directions to get there.
Hovenweep is really six different sites in a 20 mile area, with most of them being off-road and requiring hiking to. There is a nice visitor center at the Square Tower and Hovenweep Castle site.