The Library (Silence in the Library) has been suggested.
Talk about it here.
The Library was a planet-sized library that was built during the 50th century. It contained every book ever written. Within its core was the Data Core, the largest hard drive ever designed to date, which served as an index computer, as well as containing backup copies of every book ever written. The planet had one moon, which was actually an antiviral subroutine having the physical appearance of a moon. Due to its caretaking role, it was known as a Doctor Moon.
The Library and its computer was built by Felman Lux to embody his daughter Charlotte Lux' living mind before her failing body died. She could enjoy eternal life in the virtual reality, with the Doctor Moon nurturing her spiritual and mental well-being. To protect her identity and their child, the Lux family made the Library computers refer to her by the protracted name "CAL" to define the heart of its computer network. (TV: Forest of the Dead) It was managed by a head Librarian. Visitors to the Library used courtesy nodes, sculpted computer terminals containing real faces made from donated flesh; the nodes would chose a face they thought a patron would like. The security drones were levitating wooden spheres. All spheres had a camera lens and could communicate by displaying messages across a scrolling LED display in red letters. Visitors were advised to switch off their mobile comm units for the courtesy of other patrons in the library.
Paper editions of every book ever written were made specially for the Library. (TV: Silence in the Library) The forests cut down to make the books were home to Vashta Nerada, which then hatched from the books and infested the Library. When the Vashta Nerada hit their hatching cycle and began their attack, the Doctor believed someone in the Library set off an alarm that made the computer teleport everyone out of its halls and convert them into a virtual form for transmission to a safe location. However, the computer could not reconstitute anyone back to physical form, because it had no place to send them where they would be out of reach from the Vashta Nerada. Instead, the computer managed to "save" all 4022 visitors at the time to its hard drive, where they could dream an imperfect virtual existence. The virtual world was a false reality governed by fake perceptions of time and individuals, maintained by Doctor Moon, who would reassure its population there was nothing to fear, even if he had to alter memories. They would remain cut off from the real world for a century. (TV: Forest of the Dead)
Arrival of the Doctor and River Song Edit
The computer sealed off the planet to quarantine the Vashta Nerada, and it would be 100 years before the Lux family could arrange an archaeological expedition led by Professor River Song to get back inside the Library.
The Tenth Doctor and Donna Noble arrived after being asked to come by River Song, via the Doctor's psychic paper. River's expedition crew was gradually picked off and devoured by the Vashta Nerada, who began stalking the group for meat. Miss Evangelista was the first victim, followed by Proper Dave, (TV: Silence in the Library) Other Dave, and finally, Anita.
Wanting to save Donna, the Doctor tried to teleport her back to the TARDIS but she was accidentally beamed into the data core. Doctor Moon, in the form of his caretaker avatar, set up a fantasy life where she could be married and have children, but this was soon unmasked by Miss Evangelista. Her fading data ghost had been intercepted by the Library and placed into the virtual world, but it was corrupted due to being captured as it was fading away, resulting in a disfigured appearance and a staunch IQ boost. She helped Donna see through the virtual existence and reclaim her grip on the physical world.
After realising what CAL had done, the Doctor set about freeing the people trapped in the data core. After reading in the books on the Doctor's fearsome reputation, the Vashta Nerada agreed to a deal with him: they gave him a day to get everyone safely off the planet and he'd make sure the Library would be left alone for them to wander. However, the computer systems lacked the memory capacity to restore all the visitors. The Doctor attempted to use his own memory space to provide the massive transfer, but River intervened by force, knowing it would kill him. Instead, she gave her life to provide the computer enough memory to return all 4,022 people and Donna to the real world, resulting in the loss of her physical body. Luckily, the Doctor's future self retroactively planned out a way to save her from death. River's data ghost was stored on his future self's sonic screwdriver, which his present incarnation found and uploaded to CAL. River would be able to live on with her expedition crew, whose ghosts had also been captured by the computer. As the Doctor repaired the data core, Miss Evangelista also regained her appropriate looks. River then took care of CAL and two of the virtual world's children as her family. (TV: Forest of the Dead) Despite River wishing for a proper goodbye from her Doctor, he never visited the Library as he felt it would be too hard to see her again. (TV: The Name of the Doctor)
At some point after being uploaded to the Library computer, River's data ghost was able to link into a psychic "conference call" initiated by the Paternoster Gang to discuss Clarence DeMarco's message. After the "call" ended, River kept the line open between her and Clara Oswald, allowing her data ghost to project itself outside the Library to guide Clara through Trenzalore. The Doctor later displayed the ability to see this projection of River to her surprise. After getting the final goodbye she wanted, River's data ghost faded back into the Library computers. (TV: The Name of the Doctor)