Shoreditch

Shoreditch was a district of London, and the location of Coal Hill School, the I.M. Foreman junk yard, and the Shoreditch Library.

1963
The First Doctor and his granddaughter, Susan Foreman, arrived in their TARDIS circa May 1963, in the I.M. Foreman junk yard, at 76 Totter's Lane. The Doctor was in possession of the Hand of Omega. (TV: Remembrance of the Daleks, COMIC: Time & Time Again) Susan posed as a human teenager and enrolled in the Coal Hill School, and the Doctor facilitated his own studies by registering at the local library. (TV: "An Unearthly Child", The Vampires of Venice)

The two Time Lords and their TARDIS' sensors were oblivious to the arrival of two adversarial factions of Daleks and of their preparations for battle. The Doctor took advantage of the Hand of Omega's casket-like appearance, consigning it to an undertaker in preparation for burial, sometime not long before 21 November. (TV: Remembrance of the Daleks) Also in November, Lavinia Smith purchased sweets for her niece Sarah Jane Smith at a Shoreditch shop adjacent to the junk yard. Sarah Jane ventured into the yard and noticed the TARDIS' police box appearance; as the Smiths walked along the street thereafter, Sarah Jane saw Susan enter the police box. (PROSE: Playtime)

One evening, on or very shortly before 21 November 1963, two of Susan's teachers, Ian Chesterton and Barbara Wright followed her into the junk yard. Thinking that she was being held captive, the pair forced their way past the Doctor and into the TARDIS. The Doctor de-materialised the TARDIS with his three passengers, lest they be discovered by the police. (TV: "An Unearthly Child")

The Seventh Doctor returned to Shoreditch on 29 November 1963, accompanied by Ace. The pair arrived just in time to protect humanity from the 22-30 November battle between Imperial Dalek and Renegade Dalek factions in the Dalek Civil War, an event which later became known as the Shoreditch Incident. While there, the Doctor participated in the "funeral" for the Hand of Omega. (TV: Remembrance of the Daleks, PROSE: Who Killed Kennedy)

1966
After defeating WOTAN on 20 July 1966, the First Doctor returned to check that the Hand of Omega had been buried in November 1963 as per his instructions, only to discover that it had been removed. He determined that his future self had arrived at an earlier point to deal with it. (PROSE: The Rag and Bone Man's Story)

1985
In the course of trying to change Halley's Comet's trajectory and cause it to impact Earth, the Cybermen established a command post in a Shoreditch sewer in 1985. Meanwhile, the mercenary Gustave Lytton was posing as a jewel thief in order to recruit criminals to free Telos from the Cybermen. The Sixth Doctor and Peri Brown arrived in the TARDIS which appeared as ornate furniture and as a pipe organ, and defeated the Cybermen. (TV: Attack of the Cybermen)

21st century
While travelling as a companion of the Eleventh Doctor, Clara Oswald moved to Shoreditch and became a teacher at Coal Hill School. (TV: The Day of the Doctor) She continued to work there after his regeneration into the Twelfth Doctor. (TV: Into the Dalek) On one occasion, the Doctor had discovered that a Skovox Blitzer, a dangerous robot killing machine, was trapped in Shoreditch, having killed at least one local policeman. With the help of Clara as well as her fellow teacher and boyfriend, Danny Pink, the Doctor managed to neutralise the threat and return the Skovox Blitzer to space. (TV: The Caretaker)

Behind the scenes
The website whoisdoctorwho.co.uk had a list of sightings of the Doctor from which people had ostensibly been submitting to Clive, a conspiracy theorist character from Rose.

A submission from Steven Hudson claimed that Steven saw the Doctor "a couple a years ago" [sic] wearing an Edwardian outfit, rather than his usual leather jacket, but still the individual in Clive's photographs — the Ninth Doctor. He saw the Doctor wandering around a building development on Totter's Lane. According to Steven, he was muttering, "They're all gone, I'm the only one left", alluding to the Doctor's involvement in the Last Great Time War.