Yellowstone in One Day
If you plan to spend just one full day in the park, your best approach would be to concentrate on one or two of the park's major areas, such as the two biggest attractions: the famous Old Faithful geyser and the Grand Canyon of the Yellowstone. En route between these attractions, you can see geothermal activity and most likely some wildlife.
Plan on at least two hours for Old Faithful, one of the most iconic landmarks in America. Eruptions are approximately 90 minutes apart, though they can be as close as 60 minutes apart. Before and after an eruption you can explore the surrounding geyser basin and Old Faithful Inn. To the north of Old Faithful, make Grand Prismatic Spring your can't-miss geothermal stop; farther north, near Madison, veer off the road to the west to do the short Firehole Canyon Drive to see the Firehole River cut a small canyon and waterfall (Firehole Falls).
If you're arriving from the east, start with sunrise at Lake Butte, Fishing Bridge, and the wildlife-rich Hayden Valley as you cross the park counter-clockwise to Old Faithful. To try to see wolves or bears, call ahead and ask when/if rangers will be stationed at roadside turnouts with spotting scopes. Alternatively, hike any trail in the park at least 2 miles—and remember that you're entering the domain of wild and sometimes dangerous animals, so be alert and don't hike alone.
If you're entering through the North or Northeast Entrance, begin at dawn looking for wolves and other animals in Lamar Valley, then head to Tower-Roosevelt and take a horseback ride into the surrounding forest. After your ride, continue west to Mammoth Hot Springs, where you can hike the Lower Terrace Interpretive Trail past Liberty Cap and other strange, brightly colored limestone formations. If you drive 1½ miles south of the visitor center you will reach the Upper Terrace Drive for close-ups of hot springs. In the late afternoon, drive south, keeping an eye out for wildlife as you go—you're almost certain to see elk, buffalo, and possibly even a bear. Alternatively, from Tower-Roosevelt you can head south to go through Canyon Village to see the north or south rim of the Grand Canyon of the Yellowstone and its waterfalls, and then head west through Norris and Madison.
When you reach Old Faithful, you can place the famous geyser into context by walking the 1.5-mile Geyser Hill Loop. Watch the next eruption from the deck of the Old Faithful Inn.