If you have the time, go through Moab on the way. Lots of cool arches and stuff to see along the road between Moab and Bluff. Hovenweep NM takes a few hours to see but worth the trip and no crowds to fight through. Valley of the gods is a fun drive if it hasn't been raining. If you head North out of Mexican Hat on 261, you'll go up the Moki Dugway and come out at Natural Bridges. Turn right back to Blanding if your path is back through Moab. Several places to stop along that road with short hikes to Indian ruins. Go left and you'll have a very scenic drive past the top end of Lake Powell and through Hanksville.
Make sure you keep your tank full and have backup food to eat once you head south of I-70. There are a lot of things closed, like restaurants and gas stations this time of year. You are headed to the middle of no where......