About Liberty State Park in Jersey City..... http://www.libertystatepark.org/
You can easily access Liberty State Park on the NJ side via PATH trains and shuttles...this may be an easier option than going into Manhattan.
About Statue of Liberty National Park : http://www.nps.gov/stli/planyourvisit/feesandreservations.htm
Admission to the monuments is free. Parking at LSP may be $5.00. The ferry is not free...price information and suggestions for reservations can be found on the websites posted here!