The hospital is in Berkeley Springs, just a few miles from the base of the mountain. It is called Valley Health/War Memorial of Berkeley Springs, WV and it's run by Valley Health out of Winchester, VA. It is a GREAT hospital in that it is staffed by RN's for much of the patient's daily care, it's well-equipped with the latest technologies, and if the patient's need is better served at the Winchester hospital, they have an ambulance/heliport ready to go virtually immediately. Their food menus are customized for YOU. It is very, very clean, and somehow comfortable at the same time. It does not have the feel of a big city hospital, thankfully.
All this said, but please first check with the hospital if you think you have a unique physical issue to make sure they can give you the specialized care you need.
I was an in-patient there very recently, and I give the hospital a definite 5-star rating.