Reykjavik was the capital and largest city of Iceland.
In 1984, Major Whitaker of UNIT was sent by Brigadier Lethbridge-Stewart to Reykjavik to meet with Dr Iskander and investigate an unnatural increase in volcanic and seismic activity. (COMIC: The Fires Down Below)
In 2144, the Bratanian Shroud came to Reykjavik through a dimensional rift and took shelter inside the city's wireless data flow. In one timeline, the Shroud succeeded in killing the Doctor when he came to investigate. It then proceeded to summon an earlier version of the Doctor and - after murdering that Doctor - summoned the Fifth Doctor and Vislor Turlough. Working with Jill Sveinsdóttir, the Fifth Doctor shut down Reykjavik's data flow, killing the Shroud. After this, the future version of the Doctor had the knowledge of how to defeat the Shroud and was able to survive their first encounter. (AUDIO: Repeat Offender)
In 5000, the city was seized by the Supreme Alliance after the fall of the Icelandic Alliance. The Supreme Alliance itself fell after the Filipino Army advanced on the city in the Battle of Reykjavik during World War VI, an event the Fourth Doctor claimed to have participated in. (TV: The Talons of Weng-Chiang) Using information provided by his fifth incarnation, the Doctor was able to bring the brief Sixth World War to a close. (AUDIO: The Butcher of Brisbane)
In 200100, on The Weakest Link, when the Anne Droid asked Rose Tyler which Icelandic city hosted Murder Spree 20, she guessed Reykjavik, but the Anne Droid revealed it was Polar Ventura. (TV: Bad Wolf)