Elkins sits on US 33 and US 219 in the eastern half of West Virginia. It is roughly two hours by car from Morgantown, a little under three from Charleston, and about four from Washington, DC if the mountain roads are clear.
There is no useful passenger rail service. You need a car if you want to use Elkins properly, especially for Blackwater Falls, Canaan Valley, Seneca Rocks, or forest trailheads.