If this is not the most famous statue in the world, then I don't know what is (OK, maybe Michelangelo's David comes close - on a different scale, though). Everybody has seen this image many times, but actually seeing it with your own eyes is fascinating. The best experience is not the statue itself, but seeing it from up close from a ferry. I was too lazy to climb to the top, and I'm not sure if it's allowed now (certainly no elevator). The ferry does a triangle ride (Manhattan - Liberty Island - Ellis Island - Manhattan), and you should get off at Ellis Island as well, since this is really hands-on history in a very fascinating museum. I don't think the stories behind the endless immigration to America could be better presented, and maybe you'll find, as I did, that relatives you hadn't even heard of, came to the US about a century ago. I don't think Ellis Island is part of the WH site, though.