Wife and I trailered our bike from Ft. Worth to Amarillo then rode through Palo Duro last summer. The trip thru the canyon at state park speeds took about an hour. A long way out of your way for an hour ride. All of the other roads in the area are typical West TX panhandle ie; miles and miles of miles and miles.
Big Bend might be a better option. Hwy 67 from San Angelo through Stephenville is a nice cruise. Stop in Dublin and get some Real Dr. Pepper, I think it's their oldest plant and they use Cane Sugar. Tastes much better. Have fun.