You are close to Fish canyon on the Wind, (as someone already mentioned), just outside of Dubois. Fun class III at higher flows and roadside access.
Cody is about 2 hours and change from Riverton; lots of good options:
The Shoshone is great right now, 4,600 cfs and holding/rising, nice class III runs , IV+ and some real burly stuff up high.
The Clark'sfork is on its way back up,lots of quality whitewater there. Many smaller creeks are on their way up.
There are a few guys from Riverton who have been coming up here frequently the last couple of summers,can't remember names but one paddles a green Necky Chronic, (doesn't tell you much).