Located on a wooded acre of land just north of Gotham City. Full name: The Elizabeth Arkham Asylum for the Criminally Insane.
It's a combination prison and mental hospital. It has a kind of revolving door policy for supervillains. Some of the more famous repeat guests include:
DC Comics published a trade paperback by this name in 1989. It tells the story of the Joker's takeover of the Asylum and how Batman confronts both him and his own insanity.
The name 'Arkham' is taken from the works of H. P. Lovecraft.