Seeing the Statue of Liberty is a must for a first time visitor to NYC. There are multiple ways of doing this.
One way is to go to actual Statue of Liberty National Monument but that costs $19.25 for adults and $3 extra if you want to go up to the crown and you must reserve tickets in advance.
If you only want to see it and not have to pay, you can take the Staten Island Ferry round trip for free!
I did this 2 times, one during the day and one at night, not only do you get to see the Statue of Liberty, but also lower Manhattan, and for the best price. FREE!