Visiting the Statue of Liberty and going up to the Statue of Liberty is free.
Although to access the Statue of Liberty you must you must get to the Statue of Liberty via the Ellis Island Ferry, which has a fee of $12.00 for visitors ages 13 and up.
If you're over 62 years of age then the cost is $10.00 and it's $5.00 for children ages 4 through 12.
So you only need to pay the Ellis Island Ferry fee to get to the Statue of Liberty which is pretty cheap but actually seeing and visiting the Statue of Liberty or going up into the Statue of Liberty is free of charge.
You just need to pay for the access through the Ferry.
The cost is well worth it too and it's pretty sight to go up into the Statue of Liberty and I hope to be able to do so again someday.