Saratoga sits about 160km northwest of Laramie and 280km from Cheyenne. There is no public transport; a car is essential to get here and to get around once you arrive.
In summer, the drive from Laramie via Highway 130 over the Snowy Range takes roughly 90 minutes and is spectacular — worth doing in daylight. From October to Memorial Day the Snowy Range Road closes, and the year-round route runs north via Rawlins on I-80, then south on Highway 130, adding perhaps 30 minutes.
The nearest commercial airport is Laramie Regional Airport (LAR), about 90 minutes away. Denver International (DEN) is roughly four hours by road and has far more flights — most visitors coming from outside Wyoming will fly into Denver.