We stayed one night before the cruise. It cost about $50 to the terminal by Lyft/Uber.
Nice historical neighborhood. We walked to take the free ferry. The ferry runs every 30 minutes(...2:00,2:30,3:00,3:30...). Excellent view of Statue of Liberty and skyline on the ride. The ferry ride is about 25 minutes, then we walked to visit the World trade center, wall street....
The Airbnb is nice decorated. Big bedroom with a comfortable king size bed. Good quality shampoo and conditioner. Private entrance to the room. The bathroom might be a little bit tight if you are big and tall. In general, we are very happy with our stay.