Dirt/gravel capability? If so, maybe the Black Hills including the Mickelson Trail. Definitely no culture in SD.
But the scenery is pretty darn nice. And Rapid City is easy to fly into. There is a bike shop in the center of town (Cranky Jeff's) that will assemble your bike and hold your box for you then box it up for you for shipping back home.
BTW...Bad weather in the form of thunderstorms (or worse) can strike at any time most places out west.