(courtesy of Shorpy)
The only hospital radio station I could find in the United States was Radio Lollipop, a British-based charitable organization that has outlets at children's hospitals in Miami, Houston and Orange, California.
Takin' Over the Asylum is a six-part television drama about a hospital radio station. The 1994 series was produced by BBC Scotland and takes place at a fictional Glasgow psychiatric hospital called St. Jude's Asylum. The entire thing can be seen on YouTube. Episode One, Part One is below.