ITs 2 hrs each way from idaho falls to west yellowstone. You dont want to drive that road in the dark because you can run into wildlife

July 1 into SLC night Idaho falls
July 2 early AM to Jackson then to grand teton. AM you get good pics of mountains from schwahbacher landing and ox bow bend. leave around 11am, get to old faithful around 1:15pm, see old faithful area and geyser basin, night west yellowstone
july 3 north loop to norris, mammoth hot springs, LAmar Valley, and then canyon, ten return to west yellowstone then to idaho falls.

in the park --its large---30 miles=1 hr drive time. in the north loop to do this will take around 4 hrs just the driving alone.