2+ weeks heading west from Minnesota

I have an unexpected 2.5 weeks off. My wife, dog and I will be heading West from Minnesota at end of next week. We’re thinking of stopping in the Black Hills for a couple days and then going a little further west – Montana and/or Wyoming.

Ideally, we would stay below snow, and do several 3-4 day backpacking jaunts with moderate amount of driving between jaunts probable..  5+ day trips probably not on the table on this trip.

Any and all ideas welcome!! We have little Montana or Wyoming experience.