Riverton puts you about dead-even halfway between Jackson and Casper.
Jackson has tons of good playboating on the Snake and Hoback, and good III-IV+ riverrunning on the Gros Ventre and Grey's, with slightly longer drive over the Pass in to Idaho for Bitch Creek and the Teton River. After that, it all steps up a notch to solid V.
Casper has a great playpark on the Platte right in town. There is also Fremont Canyon to the southwest. After that, everything close to Casper is a step up to V and the season seems to be pretty short.
If/when you start paddling solid V, you are really close to the Popo Agie in Sinks Canyon in Lander, but it is stiff stuff. The lower is 250fpm and goes at fairly high flows (for that run), and the upper is pushing toward 550fpm and goes at lower flows. Paddle other V first, for sure. The Popo is fully "off to the races."
I haven't paddled the Wind River Canyon in years, but it is good III+ fun. I am not up on the permits needed from the Indian Reservation right now. Somebody else will probably chime in on that.
You can also go up to Cody to run the Shoshone. Short but good.
So many rivers, so little time..........