We're thinking of taking 3 weeks in September to do this circut: Denver to Arches NP to Salt Lake City to Grand Tetons NP to Yellowstone NP to Black Hills area in S. Datoka and back to Denver to see Rocky Mountain NP.

My questions are:
Is this itinerary doable in 3 weeks?
Is it possible to do this route and not make any reservations ahead of time? We'd be staying in hotels, but they don't have to be nice, just clean.
Most importantly, besides the big attractions I've listed, what suggestions do others have to see along the way? Thank you for any ideas!