Start in Bozeman , which has decent air service and is a good place to transition from the rest of the world to Montana. Use it as a place to decompress, but don’t make it your sole destination in this spectacular region.
While you’re settling in, visit the Museum of the Rockies  and spend an afternoon just wandering up and down Bozeman’s bustling Main Street. If you have a week to spend in this region, devote the first day to Bozeman.
Those with even a peripheral interest in the Lewis and Clark Expedition should plan to head to Three Forks  for day 2. Visit the Missouri Headwaters State Park , and make a side trip to the Madison Buffalo Jump, where Native Americans herded bison over the edge of a cliff. The Sacajawea Hotel  is downtown Three Forks’s biggest landmark and a fine place to spend the night.
On day 3, head south up the Madison River , around the corner at West Yellowstone (don’t bother to stop here unless you’re heading into the park), then down (north) the Gallatin River to the Big Sky  area. Either the 320 Ranch  or Buck’s T-4 make a good resting place. Stop and fish or hike.
Hike around Chico on day 6, then drive about 25 miles south to Gardiner  or Mammoth. Explore the extrahot hot springs in that part of Yellowstone.
On day seven, get up just before dawn and drive to Cooke City . As the sun rises, keep your eyes open for wolves in Yellowstone’s Lamar Valley. Continue on the Beartooth Highway to Red Lodge . If you’re continuing your journey to the east, spend the night in Red Lodge or Billings . Otherwise, make it a long day by returning to Bozeman.