I agree with most of what Hektoglider said.
Chief Joseph, the Beartooth and the Bighorns are not to be missed and you'll save yourself some coin by not having to pay the entrance fee (and traffic) to Yellowstone by following this route
, where you stay a night at a nice little Nat Forest campground near Burgess Junction (Sibley Lake
), where there is a good restaurant and gas
close by at Burgess Junction. Next day, ride the Medicine Wheel Passage over to Cody and then pick up 276/US 212 to Red Lodge and then take 78 to Columbus, MT where there is a free city campground
alongside of the Yellowstone R, just over the bridge, on your right. Then head on up to Great Falls the next day.