Liberty Harbor is a big parking lot with services (water/electric) and a dump station. It is expensive ($80ish) per night. Those are the bad things.
The good things. It is located in the perfect spot for viewing the Statue of Liberty, especially at night. It is right in the city (Jersey City). There is a water taxi that leaves every 30 minutes from the marina at Liberty Harbor ($8.00ish) that goes to Wall St. or you can walk 2 blocks to the PATH train ($2.50ish) and go directly to the World Trade Center. It takes about 5 minutes.
We spent 5 days there and it is definitely NOT a destination campground, but you can't get any closer or have a better location for exploring the city.
The walk to the PATH is very safe and goes through a residential neighborhood. I didn't feel the least bit unsafe walking with my then 9 and 6 year old girls and DH. Lots of young working adults out walking dogs until late at night and security guards at the marina.