There's no way to get to the Sawtooths at Stanley, ID without a climb and/or descent. The easiest would be at Twin Falls 93/26 to 93 toward Challis and then west on 75 to Stanley. You will have Willow Creek Divide on 93 just south of Challis with 3-5% grades for approx 3-4 miles which is mild for the western mountains.
Coming up through Sun Valley on 75 you would have Galena Summit with 6% grade.
To get to Teton Nat'l Park from Stanley, ID. go east on 75 to 93 toward Arco then 20 east to Idaho Falls and pick up 26 east to Alpine then north on 26/89 into Jackson, WY - a nice easy drive.
Caution: If looking at a map do not take a shortcut off 26 at Swan Valley, ID and picking up 31/22 into Jackson. You definitely will not like coming down Teton Pass!
From Jackson into Teton Nat'l Park is an easy drive, as well. If you can dry camp we really enjoy Gros Ventre campground in Teton NP. It has 300 sites; no reservations but rarely fills. There's another similar campground farther north into the park called Colter Bay campground. It's next door to the hookup RV park called Colter RV - need reservations for this one.
The Sawtooths and Teton NP are favorite areas of our. Enjoy! Don't forget Yellowstone which you can enter from Teton NP.
Full-timed for 16 Years . . .
Traveled 8 yr in a 2004 Newmar Dutch Star 40' Diesel
& 8 yr in a 33' Travel Supreme 5th wheel