My preferred route from Casper is route 20 to Shoshoni, then route 26 over the Togwotee Pass to Moran Junction in Grand Teton National park, then route 191 to the south entrance of Yellowstone. Route 26 begins a gradual climb around Dubois to the pass then a gradual descent to Grand Teton. Route 191 begins a gradual climb after passing Jackson Lake, then descends to the south entrance station, then climbs again along the Lewis River Canyon to reach the plateau at Lewis Lake. From there it's just minor hills to West Thumb Junction, then pretty much level around the edge of the lake to Fishing Bridge. Nothing I would consider serious mountain driving on this route.
Spend some time in Grand Teton while you are in the area - it's our favorite place.
2003 Winnebago Minnie 24F - Ford E-450๐