Stormcage Containment Facility

Stormcage Containment Facility was a prison in the 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. By the 53rd century, a Stormcage (perhaps one of many) had been renovated, and became known as the Hesguard Institute (COMIC: Sin-Eaters)

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. River was eventually pardoned and released after the Doctor erased all knowledge of himself from every database in the universe thus causing there to be no proof River ever actually killed anyone.

History
At an unknown point in time, River was apprehended and imprisoned there (TV: The Time of Angels) for killing the Eleventh Doctor at Lake Silencio in Utah, the United States, 2011. (TV: The Wedding of River Song) 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 to Stormcage via her Vortex manipulator by the Doctor as she was interfering with their first date. (TV: Last Night)

On another occasion, the Doctor, Alice Obiefune, the Squire and Abslom Daak broke River out for her assistance in a mission. (COMIC: The Judas Goatee, The One)

At an unknown point in River's timeline, the TARDIS itself contacted River, ringing the Cloister Bell over the phone, when the Doctor had become separated from his TARDIS by a time storm and trapped below the Bank of London. River used her hallucinogenic lipstick to sneak past the guards to the security office, recover her vortex manipulator and sonic blaster, and escape to rescue the Doctor. (GAME: The Eternity Clock)

Eventually River was released the custody of Father Octavian, who wanted her to go back in time to the 51st century with him to assist in a mission involving Weeping Angels. She could provide the equivalent of an army with 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)

In the 53rd century, a Stormcage Containment Facility was renovated and renamed. Now known as the Hesguard Institute, it aimed to "cure" prisoners of their criminal ways by removing all of the prisoner's negative emotions and depositing them into another body, known as a Sin-Eater. When they tried this treatment on the Doctor, his Sin-Eater became conscious and helped awaken the other Sin-Eaters in the prison. (COMIC: Sin-Eaters)

Security
Stormcage was situated on an unknown planet on which a storm perpetually raged, although at times it also had a snowy climate. (COMIC: The Judas Goatee) The facility was regularly patrolled by guards equipped with blasters; although well-trained, River frequently managed to give them the slip through the use of her hallucinogenic lipstick, despite announcements by loudspeaker about this kind of danger.

Electronic security scanners frequently swept the facility hallways; these scanners identified escaped prisoners through facial recognition when caught within their beams and set off alarms to summon guards to the area.

The entire facility was surrounded by a Tesla binding field, which prevents escape from within by use of Transmat or vortex manipulator. (GAME: The Eternity Clock)

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  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.