Royal Leadworth Hospital was the local hospital in Leadworth. It was the main location of a confrontation between the Eleventh Doctor and Prisoner Zero, who was using patients in the coma ward of the hospital to effect disguises to evade recapture by the Atraxi. Rory Williams was a nurse at the facility. Dr. Ramsden was at least an on-call doctor at the institution. Many doctors were killed by Prisoner Zero during his rampage here, including Dr. Ramsden.
The Doctor was not a patient of the hospital, but he completed his regenerative cycle there while engaged with the Atraxi. He also stole clothing from the staff locker room, in much the same way that his third and eighth incarnations had done previously after their regenerations, deciding on their basic "looks" from clothing stolen from hospitals. Only this time, Rory, being one of the staff, weakly protested his theft; the Doctor ignored him. (TV: The Eleventh Hour)
Behind the scenes
Though the production team took the time to provide a sign for the hospital, it is not especially visible in any shot that survived in the final cut of the episode. The name of this facility is instead plainly visible on Rory's ID badge.
A Notice of Theft was put out by the Administration Office concerning the clothing the Doctor took from the First Floor Secure Locker Room. The notice stated that the clothes were stolen on 25 June. (REF: The Doctor: His Lives and Times)