The Statue of Liberty was a landmark located on an island in the river contiguous to New York City, and in an alternate timeline was secretly transformed into a Weeping Angel, many of whom which were using the city as a "farm".
Biography
The Doctor was only known to have visited the Statue of Liberty in situ once. In 1930, the Doctor's TARDIS materialised at the base of the Statue, and remained parked there while the Tenth Doctor and Martha fought an attempt by the Cult of Skaro to rebuild the Dalek race. In showing off the Statue to Martha, the Doctor quoted from the Statue's famous inscription, saying, "Give me your tired, your poor, your huddled masses, yearning to breathe free." (TV: Daleks in Manhattan)
In the Doctor's eighth incarnation, the Threshold took the Statue of Liberty and other items of Earth culture to the town of Wormwood on the Moon. (COMIC: Wormwood)
In an alternate timeline where the Weeping Angels created a "time energy farm" in New York City, they were able to use this energy to transform every statue in the city into Angels. Eventually, this included the Statue of Liberty. Sometimes, when the Weeping Angels imprisoned victims in Winter Quay to use as food by constantly sending them back in time, the Statue of Liberty would travel from Liberty Island to the Quay. In 1938, when Rory Williams and Amy Pond, whom the Angels had recently trapped in the Quay, jumped from the Quay's roof (to negate an alternate timeline in which Rory remained imprisoned at Winter Quay for the rest of his life), the paradox this created poisoned and killed the majority of the Weeping Angels at Winter Quay, including the Statue of Liberty. Following this, the Statue became an inanimate object. (TV: The Angels Take Manhattan)
Alternate timeline
In an alternative timeline in which Morbius conquered Earth, he took the Statue of Liberty in order to have it installed atop the palace of Morbius on Karn; this timeline was later erased from reality. (AUDIO: The Vengeance of Morbius)
Mentions and other appearances
The Doctor occasionally encountered it at different locations, or at least referenced its iconic design, at other points in his life. In his fifth body, he compared a statue of the Divine Empress of the Earth Empire to the Statue of Liberty on Earth. (PROSE: Cold Fusion)
During his tenth life, the Doctor noted that one of the features of the Gameslaves' pinball table was a life-sized Statue of Liberty. (COMIC: Pinball Wizard)