An island was a body of land completely surrounded by water.
Irving Braxiatel created a floating island which he dubbed Laputa, stationing it near Venice, Italy in 1609. The Armageddon Convention was held there. (PROSE: The Empire of Glass)
The Fourth Doctor and Leela visited Easter Island in 1872. (PROSE: Eye of Heaven) River Song said the Eleventh Doctor was worshipped there when they visited it. (TV: The Impossible Astronaut)
There was a Silurian colony beneath the Galápagos Islands, which revived during Charles Darwin's visit in 1835. (AUDIO: Bloodtide)
Jack Harkness visited Ellis Island at least twice. The first time was in 1892, where he experienced his second death and realised he was immortal. (TV: Utopia) The second was in 1927, where he met Angelo Colasanto. (TV: Immortal Sins)