Alpha Centauri (planet)

Alpha Centauri was the home planet of the Alpha Centauran race. (TV: The Curse of Peladon, et. al) Alpha Centauri did not have any natural predators. As such, Alpha Centaurans were free to develop skills in politics and focus on politeness. (PROSE: The Monster Vault) The world was also a part of the Galactic Federation and served as its headquarters in 3375. (TV: The Curse of Peladon, The Monster of Peladon, PROSE: The Dark Path)

History
When the Cybermen allied with Rassilon to rewrite all of history, Alpha Centauri was rendered lifeless by Cyberman forces. This version of history was undone by the Twelfth Doctor and Rassilon. (COMIC: Supremacy of the Cybermen)

At some point, Alpha Centauri was host to annual Alpha Centauri Olympics. (AUDIO: A Requiem for the Doctor)

When the Second Doctor landed in Australia in 2018, he was actually trying to get to either William Shakespeare's house in Stratford-upon-Avon or the Pan-Galactic Games on Alpha Centauri, as Jamie McCrimmon had wanted some excitement and spectacle. (PROSE: Timewyrm: Apocalypse)

In 2019, Maxie Masters, who had previously become a political exile from her home planet Gendar to take refuge on Earth, briefly irrationally considered fleeing Earth for Alpha Centauri when she thought she was in trouble with Giles. (PROSE: Out of the Box)

From invalid sources
In an untitled Doctor Who minisode broadcast as part of Tonight's the Night, Jack Harkness mentioned once having gone to a party on Alpha Centauri.

In the story of Doctor Who: Legacy, the Eighth Doctor mentions humanity spreading to Alpha Centauri.