Grand Canyon of Yellowstone is the second most popular attraction other than the geysers of the park. A single trail runs across the north and the south side of the canyon, spawning the idea for this route.
My proposed route North to South is from Inspiration Point to Point Sublime on the other side of the canyon. Both of these lookouts are dead ends to the respective trails and thus natural bookends to the end of the run. The Yellowstone river must be crossed at the Chittenden Bridge.
Some may prefer Artist Point as the South endpoint, due to the fact that in order to run South to North, runners must park and walk to start at Point Sublime.