Yellowstone to Cody is pretty easy, because you haven't been over the Bighorns going east. Personally, I'm uncomfortable pulling my Jeep toad with a 'C' on any road that has pullouts that have "pull over to check your brakes" signs at the top of each descent. I'm a flatlander from the east and I go north to I-90E and spend some time in the Black Hills on the way home.
BTW, Sturgis is August 3rd - 9th this year. Traffic in the area is heavy, but you won't be able to find an open spot in a CG. But the scenery is nice. :)