Here is what I found at Subaru.com
Its in Jackson Hole and would seam to be the closest.
This one is in Idaho Falls. Depending on where in the Park you are stationed could depend on which one is Easyer or has the best Road for following the twistys out side of the park. It looks like you can make the run to Idaho falls faster if you are closer to West Yellowstone. Hey you got all summer to figure out which drive is better for you
Enjoy your stay out here in the West.