Set your alarm for 5am. This is non-negotiable. Drive into Yellowstone through the north entrance and head east toward Lamar Valley — the widest, flattest, most wildlife-rich valley in the park, sometimes called the American Serengeti, which is hyperbole that the valley sometimes justifies. The wolf packs that were reintroduced here in 1995 and 1996 changed the entire ecosystem: the elk changed their grazing patterns, the willows and aspens grew back along the riverbanks, the beavers returned, the songbirds returned. This is called a trophic cascade and Lamar Valley is one of the most studied examples of it on the planet. You will almost certainly see bison. You may see wolves or coyotes or grizzly bears or all three. Pull over whenever anyone else has pulled over. The spotting scopes line the valley at dawn and the wolf watchers — a dedicated, deeply knowledgeable community who camp here for weeks — will tell you what they're seeing.
Exit the park through the northeast entrance at Cooke City and pick up US-212 east — the Beartooth Highway, which Charles Kuralt called the most beautiful drive in America and which has never been seriously challenged for the title. The road climbs from 7,500 feet at Cooke City to 10,947 feet at Beartooth Pass in 25 miles, through a series of switchbacks so steep they have their own names, past alpine lakes and tundra and snowfields that persist into August and granite peaks that look like the surface of the moon if the moon had wildflowers. At the pass there is a parking area and a view south that shows you where you've been: the full Beartooth Plateau, 900,000 acres of high alpine wilderness, and somewhere in it, the valley where the wolves were reintroduced thirty years ago and changed everything.
Descend to Red Lodge, Montana — a former coal mining town turned mountain resort with a good Main Street and a late breakfast place called Red Lodge Café that makes the kind of pancakes that justify the stop. Sit for an hour. You've earned it. Then drive north on US-212 and I-90 toward Bozeman, two hours away, through the Paradise Valley along the Yellowstone River, past the Absaroka Range one last time, and into the college town that has been the most livable city in Montana for long enough that it's no longer a secret.
Dinner in Bozeman: Nova Café for breakfast-all-day if you arrive early, or Blackbird Kitchen for something more substantial in the evening. The trip is over. The Beartooth is still in your head. That will take a while to fade, and it should.