During the Shoreditch Incident of 1963, the Imperial Dalek mothership entered a powered geostationary orbit of Earth. (TV: Remembrance of the Daleks)
The Tenth Doctor claimed it was impossible for the planet Krop Tor to be in geostationary orbit around a black hole, as it should have been pulled in like the star systems around it were. He calculated that it would have taken a phenomenal amount of power to generate the huge gravity field stabilising its orbit. (TV: The Impossible Planet)
In the far future, the Pridka Dream Centre was in geostationary orbit above the second planet in the Taprid system (PROSE: Infinite Requiem) and Zellin's space platform was in geostationary orbit. (TV: Can You Hear Me?)