So there is a small town about 80 miles from the Four Corners region, named Mexican Hat in Utah, and if you blink you will miss it. There is a gas station, a place to buy beer, a few lodging establishments and that’s about it.
But the it is in the desert, and that is quite interesting. Monument Valley is 26 miles away, Goosenecks State Park is 8 miles and it most famous sight in the vicinity is the Mexican Hat rock, mostly because they named the whole town after it.
We did this trip in a Mini Cooper S. The Mini was perfect, a great balance of fuel economy, ground clearance and power. Loved the car and loved the sights!