Arkham Asylum

Arkham Asylum is a mental institution that contains and treats the criminally insane people of Gotham City, housing hundreds of deluded maniacs, most of which are iconic enemies from the Batman franchise.

Though not intentionally a villainous hideout, Arkham is basically just a secure planning ground for the homicidal foes of the Dark Knight, as well as a place of undeserved power for the sadistic, obsessive warden, Quincy Sharp. These foes are most notably listed as the Joker, the Scarecrow (who was formerly a doctor at the institution), the Riddler, the Penguin, the Mad Hatter, and many more.

Trivia

 * It is based off writer H.P Lovecraft's telling of the asylum, which was based off a real-life, currently demolished maniac treating facility called the Danvers State Hospital.