The stretch between Park City, UT and Jackson WY offers a ton of sights to be seen, A few of these include: Craters of the Moon National Park in Arco, the Mormon Temple in idaho Falls and Mesa Falls. If you can sneak into the Tetons south of there on back roads near Driggs (although the roads don't go through). The Snake River Gorge by Twin Falls is also really beautiful, and Twin Falls itself is a nice town to stop and eat at.
A few other places worth seeing are the Old State Penitentiary, Idaho's Secret Park (Wildlife Refuge), Coeur d'Alene's Old Mission (oldest building in Idaho), Minnetonka Cave and Rainey Creek which is home of the World Famous Square Ice Cream Cone.
The lava trails at Craters of the Moon are so cool...it truly feels as if you are on the moon. Before visiting the Moon, head to the visitors centre and have a visit there to talk to the rangers and see the mini-museum there which has cool exhibits on volcanology and nature.