We have stayed at Liberty Harbor twice and will do so again when we travel back to that coast. You can see the Statue of Liberty from the RV park but not the side you normally see shown on TV. You can see her back.
Assuming you haven't done NYC - you can take a ferry from the park or a train (subway type) a couple of blocks from the RV park to get to downtown NYC. It you are going to be in that area touring NYC I'd suggest you buy a three day ticket (or two or four) on one of the city tour buses - on and off where ever you want - and the tour bus ticket usually includes other things such as museums, Empire State Building, Liberty Island, museums, harbor tours, etc. On our two trips we just didn't have the time or energy to use all the options. We found the people in the NYC area to be very friendly and helpful (unlike the stories we heard 30 or 40 years ago). We were having trouble figuring out the ticket machine and a "local" came over, asked what we were trying to do, and then helped us do it. Rush hour is extremely crowded.
Bob, Sandi & Marmaduke the Big Pug
SW OREGON 2004 Journey 39K, 330 Cat
If towing: a 2006 Mini Cooper or 1995 Wrangler