The Statue of Liberty, or Liberty Enlightening the World, is a large statue located near New York City on an island at the mouth of the Hudson River in New York Harbor.
The statue was given to the people of the United States of America by France, and was completed in 1886. Originally a symbol of America's unique freedoms and liberties, the Statue of Liberty later came to be accepted as a symbol of the principles of liberty espoused by United Earth and by the United Federation of Planets.
Due to New York City's importance to Earth it was repeatedly attacked during World War III. The statue was destroyed. After the end of the war, the New Statue of Liberty was built. (Last Unicorn RPG module: A Cadet's Guide to Sector 001 Earth)
In 2375, Admiral Leonard McCoy and Captain Montgomery Scott piloted a runabout to New York City following the Breen attack on Earth, and were heartened to find, despite the minor damage to the rest of the city that "Lady Liberty" was intact. (TOS short story: "Safe Harbors")
Despite the reference of it being destroyed in the Last Unicorn RPG module, McCoy's observations suggest that he is looking at the original, not a reconstruction.
The Na'kuhl once attempted to interfere in human history, giving assistance to Nazi Germany during the Second World War. As a result of this assistance, the Nazis were able to invade and conquer a large portion of the eastern United States. Adolf Hitler visited the Statue of Liberty in 1944. Fortunately the Nakul were thwarted by Captain Jonathan Archer and the Enterprise, and the timeline was erased from history. (ENT episode: "Storm Front")
On Earth in an alternate reality, a landing party from the USS Enterprise encountered a half-buried Statue of Liberty. An astronaut from that world, George Taylor, told James Kirk that he thought he had landed on an alien world until he saw the statue. (TOS comic: "The Primate Directive, Issue 2")