We took I-80 to Cheyenne WY, then north on I-25 to Casper, then US26 west to either Riverton WY or Dubois WY and took the toad into Tetons Park. In Riverton we stayed at the Wind River RV Park. Not fancy but suited our needs. The 2nd trip we drove on to Dubois WY and stayed at the KOA. Love the little town of Dubois. If you saw the movie "Taking Chance" with Kevin Bacon, Chance Phelps is buried at the cemetery in Dubois.
When we left Dubois, we backtracked to US20 north to US16-20, then US 20 west to Cody. We stayed at the Yellowstone Valley Inn on US16-20 about 35 miles from the Yellowstone entrance. We drove it easily each day, or you can continue on if you're staying inside Yellowstone. I would highly recommend visiting Cody WY to see the Buffalo Bill museum. You can either drive from Yellowstone Valley Inn RV Park or stay in Cody. You should make reservations either way as we tried to stay in Cody but they were booked solid.