Here is my answer to the 6/11/18 question on the Quora website: What are some sights to see in two days at Yellowstone National Park? (BTW, Two days is not nearly enough for a place as large as Yellowstone.)
The century-long-and-then-some favorites are the Grand Canyon of the Yellowstone River with its two great waterfalls and Old Faithful Geyser. But before or after the always-predictable Old Faithful eruption take the Geyser Hill walk with or without an interpretive ranger and enjoy lovely hot springs and the possibility of other geysers going off. The other most remarkable sight near Old Faithful (a few miles north of it) is Midway Geyser Basin, but you *must* get there early or late in the day to find parking.
Be ready to stop as you drive between these major attractions, since there are pleasant surprises (sometimes including wildlife) all along the roads.
Photo credit: Grand Prismatic Spring in Midway Geyser Basin, taken by Bruno Giletti, can be seen on page 65 of Yellowstone Treasures, updated fifth edition.