Stormcage Containment Facility

Stormcage Containment Facility was a prison in the 51st and 52nd century of the highest security. River Song was a prisoner there and a frequent escapee, but always returned as her part of the charade to make the Silence think she actually killed the Doctor at Lake Silencio.

Though the staff were able to keep most of the prisoners in their cells, they failed endlessly with River Song, However, as she always returned after a breakout, they might have eventually given up on trying to stop her and left her to her own agenda.

History
At an unknown point in time, River was apprehended and imprisoned there for killing the Eleventh Doctor at Lake Silencio in Utah, the United States, 2011. They gave her twelve thousand consecutive life sentences as punishment.

On her first night, River was sprung from prison by her husband to go on their first date together. She was later returned after learning about her diary. (TV: First Night)

In 5145, River escaped from Stormcage to warn the Doctor about the Pandorica opening and the TARDIS exploding after receiving a call from Winston Churchill which the TARDIS had redirected to her. (TV: The Pandorica Opens) She returned of her own free will after leaving the Doctor confused about her marital status following his remembrance back into the universe, but in an earlier century. (TV: The Big Bang)

At an uncertain time, River left from Stormcage to spend her birthday with the Doctor on an ice-skating trip and watch a performance by Stevie Wonder, who was unknowingly taken to 1814 to perform. After being returned to Stormcage, River set off an alarm, which was quickly turned off when she informed them it was she, returning to her cell. Rory, having been sent by an earlier Doctor to assist in the battle of Demon's Run, was waiting for her. Knowing what would happen there, River declined, explaining that she could only be there at the end. (TV: A Good Man Goes to War)

Later in the 52nd century, River received a letter from the Doctor, asking her to meet him in America 2011. She escaped from Stormcage with ease. (TV: The Impossible Astronaut) After they defeated the Silence's occupation of Earth, the Doctor returned River to Stormcage. (TV: Day of the Moon)

At another unspecified time, River was returned here via her Vortex manipulator by the Doctor as she was interfering with their first date. (TV: ''Last Night)

In the 51st century, River was released in the custody of Father Octavian, who wanted her assistance in a mission involving Weeping Angels. She could provide the equivalent of an army in the Doctor. When their mission was over, River was presumably returned to Stormcage, though she hoped she had done enough to earn a pardon. (TV: The Time of Angels / Flesh and Stone)

At some point afterwards, River was indeed pardoned and released from Stormcage as there was no longer any evidence that the Doctor existed at all due to him erasing all evidence of himself from every database in the universe as part of his return to the shadows. (TV: The Angels Take Manhattan)

Behind the scenes

 * According to an interview with Alex Kingston, she thinks Stormcage is some kind of a prison planet and it is particularly unpleasant to stay there. Through the window of River's cell, heavy rain can be seen.
 * According to the commentary track of TV: A Good Man Goes to War, the lower level of the Millennium Stadium in Cardiff is used for shooting the section of Stormcage in which River is held.