Idaho
Idaho is a wild, free, and sparsly backpacked place for the most part. We think the best two spots are the Bighorn Crags, in the Salmons, northwest of Challis, and the White Clouds Peaks, across the highway from the overly visited but still recomended Sawtooths (the town of Stanley is worth a look). Or, take the entire loop around the Seven Devils, and scramble up a couple, maybe. From some places here you can see back across the Snake River in Hell’s Canyon to the Wallowas in Oregon, where most of the precipitation stops.
Strictly speaking, the “backside of the Tetons” are in Wyoming, but accessed from Idaho, and deserve attention. Idaho shares the Bitterroots with her more quickly accessible Montana side. The photographically challenged can get a picture standing in two states right on her crest.
Good trips in these mountains? Bighorn Crags, Boulder Chain Lakes, Yellow Belly, Sheep Lake and She Devil, Alaska Basin, and Big Creek/Bear Creek.
This is rugged, dry, pink and white granite looking craggy country, excepting the lush Bitterroots. Huge elk may be seen.

Castle Peak, White Clouds, Idaho in late June