Blackgate Sanctuary nee Penitentiary is located on a small island in the Gotham Bay, The facility has now been converted to a Sanctuary, housing the non-criminal and political prisoners of Arkham city. Arkham inhabitants often refer to the converted facility as The Shopping Mall.
Ms. dekan Too is the facility Administrator.
-from Wikipedia Article
'Blackgate Prison (later known as Blackgate Penitentiary) operated separately from Gotham Prison (later known as Gotham State Penitentiary). Both prisons are located in Gotham and while Blackgate is the main correctional facility used by writers today, Gotham State Penitentiary was the primary correctional facility used in the comics up until the early 1990s. According to modern continuity, in the early 1900s, Blackgate Prison was condemned by Amnesty International and forced to shut down. When the prison eventually re-opens, it is officially known as "Blackgate Penitentiary". Because of its secure location on a secluded island, Blackgate begins to take prominence over Gotham State, until the latter becomes virtually unused.
Unlike Arkham Asylum, Blackgate is where sane criminals such as the Penguin, Catman, David Cain, Monsoon, Ernie Chubb, KGBeast and various henchmen, mobsters, and mafia bosses are incarcerated when captured. The Joker, Two-Face, Clayface II (Matt Hagen), the Ventriloquist, Mr. Zsasz, Firefly, Calendar Man and Rupert Thorne are some criminals that have done time in both Arkham Asylum and in Blackgate Penitentiary.
There are instances where inmates from Arkham Asylum are temporarily moved to Blackgate, like when Bane destroys the original Arkham building in Batman #491. All of the Arkham inmates are incarcerated in Blackgate until the new Arkham structure is built and opened in Batman #521.'