A recent National Public Radio piece on the "hidden" half-sister of Cindy McCain yielded this tidbit about their father, James Hensley:
Documents show Kathleen Anne Hensley was born to Jim and Mary Jeanne Hensley on Feb. 23, 1943. They had been married for six years when Kathleen was born.
Jim Hensley was a bombardier on a B-17, flying over Europe during World War II.
He was injured and sent to a facility in West Virginia to recuperate. During that time, while still married to Mary Jeanne, Hensley met another woman — Marguerite Smith. Jim divorced Mary Jeanne and married Marguerite in 1945.
Cindy Lou Hensley was born nine years later, in 1954.
Note: the Wikipedia article identifies Cindy McCain's mother as "Marguerite "Smitty" Hensley (née Johnson)."
As for a guess about the Mountain State facility, Wikipedia also says that The Greenbrier resort served as an Army hospital during World War II.