Next stop on the way to those 4 corners is Natural Bridges National Monument, a small, isolated Utah park with these huge natural bridges. This is a great park, easy to do, and you will be mostly alone here. These bridges are carved by water making them technically different from the arches at the other Utah parks.
After that, I headed down Utah 261, 22 miles of freshly paved highway that goes to or through no towns and then ends abruptly at the top of a cliff. Pavement ends, gravel begins, and then you pretty much drop down the side of the cliff. I have done many amazing roads over the years but this is as exciting and scary as any! And then, when you reach the canyon floor, the pavement begins anew and off you go like nothing happened.