https://www.tripadvisor.com/HotelsNear-g54171-d7840847-The_Medical_University_of_South_Carolina-Charleston_South_Carolina.html. visit that link, they'll be multiple choices.
The hospital has a partnership with some hotels just across the river with special rates. We stay the night before but I would not leave my child unattended overnight at the hospital itself... They have chairs and a couch in the kid's rooms.
The closest would be in N. Charleston which would be 25 minutes
The staff actually provides you a room if you are in an emergency
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