We have used route 191 a couple of times in the past. Just some rolling hills with the Wind River mountains far in the distance to the east. That said, our preferred route is 26 from Casper all the way to Moran Junction in Grand Teton NP. Route 26 goes over the Togwotee Pass but the climb is gradual beginning at Dubois with great scenery along the way.
X2 on TexasShadow's suggestion for Gros Ventre campground in the Park. In our many trips we have never had an issue getting a site there, even in July. FYI, we paid $92 for a site at the Virginian campground back in 2016.