If you want to see the Statue of Liberty without a visit to the monument itself, but also make some amazing photos, not only those of Statue of Liberty, but also of the Lower Manhattan, the Brooklyn Bridge and the Verrazano Bridge, take a trip on the Staten Island Ferry. It is absolutely free, and even might be used as a great opportunity to get some rest, in case you walked a lot through the nearby Wall Street, or did shopping at Century 21, which is just a 10 to 15-minute walk from the ferry.
The Staten Island Ferry connects Manhattan and Staten Island. To get to the Staten Island Ferry from the Manhattan side, you need to get off at the South Ferry and Whitehall subway stop (look at the bottom of Manhattan map). It’s next to Battery Park. The trip takes 30 minutes one way; there are many open areas on the ferry and enough space for everyone.
There will be a lot of people waiting for a ferry at the station building. No worries, everyone will fit in, and it will not be crowded on the ferry. When it arrives in Staten Island, all passengers will be asked to leave the ferry. You will need to go out to the station building on Staten Island and then board the ferry again. Schedule and news can be found on the ferry’s website.