This is one of the most identifiable entries on the whole list. It is a great feat of engineering which is inextricably linked with a political philosophy, representing a significant change in human migration.
In June 2009 I revisited the Statue of Liberty some 12 years after my first visit, on my initial trip I got onto Liberty Island and into the base of the statue. The main impression I can remember was that the statue was large and the queues were long. My second trip enabled me to confirm these initial thoughts. There were incredibly long queues to get out to the island, as such I used the free Staten Island Ferry to get a closer view of the statue and found this a good compliment to my earlier trip. If I was visiting for the first time I would be tempted to join the long lines and security screenings to get closer to the island, but as I had already seen it up close I was happy to sail by with a large number of commuters into Manhattan.
This is one of the most overtly political inscriptions on the list; I wonder if other particularly ideologically charged monuments would get onto the list? However migration to the United States in the first 150/200 years of its existence was one of the greatest unforced (mostly) movements of people in human history and as such is a worthy event for such a renowned monument.
I really enjoyed New York; it certainly has a real buzz about it. Despite the huge buildings it feels distinctly human, partly because it is surprisingly grubby in places (and that isn't a criticism). Many major western cities, especially some of the American cities I have visited, really lack an atmosphere as the wide roads and tall buildings remove the human scale of the city. New York doesn't suffer from this, and I found it a really rewarding city to visit, and the Statue of Liberty was one of the highlights for me.