The Bannock County Historical Museum is the old-school kind of local museum: cases of objects, period rooms, photographs, and donated pieces that together tell the story of a place. The exhibits cover the Oregon Trail, railroads, military history, ranching, and daily life in southeast Idaho.
It sits beside Fort Hall Replica in the Ross Park area, so it is easy to visit both in one stop. Give it an hour if you like local history; less if you are only looking for the broad strokes.