Just as a side note, Yellowstone is about 5-6 hours from Salt Lake City. I live in Utah, near the Flaming Gorge, and it takes us about 4 hours to drive to Jackson Hole; another 45 minutes to Yellowstone. Beautiful country! West Yellowstone in the fall is simply magnificent with the changing colors of the leaves.
Which does remind me, to make the most of these side trips, time-wise, you (the OP) would want to rent an automobile.