A way to see the Statue of Liberty for free is to take a ride on the Staten Island Ferry. The ferry takes us from the Whitehall Terminal Manhattan to St. George Terminal Staten Island (and back to Manhattan). Since there are numerous ferry departure times, there really isn't a need to check the timing beforehand.
Looking back at the Manhattan terminal docks as the ferry is departing.
View of the Brooklyn coastline from the ferry.
Another Staten Island Ferry traveling in our opposite direction back to Manhattan.
View of the statue with Jersey City in the background.
Statue of Liberty against the setting sun.