Autokelly,

Start in Billings and go 60 miles south to Red Lodge. Day 2, up over the Beartooth pass to Cooke City (60 miles and an elevation gain of 4000 ft.). Day 3, Cooke city to Mammouth Hot Springs at the north entrance to Yellowstone National Park (50 miles or so all through Yellowstone). Day 4, Up Paradise Valley to Livingstone, MT. 69 miles. You can't get any better than this.