The Legacy Flight Museum sits at the Rexburg-Madison County Airport on the north side of town and houses a collection of airworthy and static WWII-era aircraft alongside exhibits on Idaho aviation history. It's a modest operation — this is not the Air Force Museum in Dayton — but what's here is well-presented and enthusiastically maintained. The aircraft on display have included a P-51 Mustang and a T-6 Texan among others, and the volunteers who staff the place tend to know their material.
If you are travelling with children who have any interest in aircraft, or if you have a passing interest in WWII aviation yourself, the museum is worth the short drive from town. Flying demonstrations are sometimes held in summer. Call ahead or check their schedule online before visiting, as hours can be irregular outside the peak season. Admission is inexpensive and the airport setting — small, quiet, with the Snake River Plain stretching away in all directions — has its own charm.