Frank Church River of No Return Wilderness -- follows the Snake River through Hells Canyon (as deep as 9,300 feet, much deeper than the Grand Canyon) north towards Lewiston, where the Clearwater and Snake River meet
Yellowstone National Park -- Second only to Yosemite as the most majestic National Park in the lower 48 states, but weirder, more colorful, and more spectacular, filled with hot springs, geysers, and fumaroles. Mostly within Wyoming, but the most notable feature, Old Faithful is probably most easily reached from Idaho Falls via West Yellowstone, Montana - though the park road is only open in summer (May to early November).
The Nez Perce Indian Reservation, home to Native Americans whose forebears helped Lewis and Clark through the winter during their expedition, is just East of Lewiston.
City of Rocks National Reserve -- Located on the southern edge of the state. Popular with hikers and rock climbers for its maze of massive boulders (some over 100 meters in height).