According to the MCU wiki, Claire works at the Metropolitan-General Hospital, located somewhere in Midtown. It does not exist. The two other hospitals mentioned in Condemned, Mercy and St. Mary's, are also fictional. (Or at least, there used to be an Our Lady of Mercy in the Bronx, and a St. Mary's in Brooklyn, but both are closed/renamed and it wouldn't make any sense to send ambulances to either from Midtown Manhattan).