Cheyenne, Wy , then over to Rawlins US 287 then US 26 would be my route.
I very much agree with this recommendation. Last September we stayed at Lander, WY at the Sleeping Bear RV, but we have also stayed at Dubose. There is a fine park there.
The view of the Tetons from Togwotee Pass is not to be missed. There is a nice parking area adequate for big rigs. We had lunch there in September. Even if you don't stop in the Tetons, it is a great drive on into Yellowstone. As for us we stopped this time at Colter Bay. We did drive into Yellowstone for a day trip, but Colter Bay was our destination this time.
We have stayed in Rawlins, but coming from Denver you could easily make it to Lander or even Dubose.