Hi there...there are places in Jersey to stay, but not near the Statue of Liberty.
Like Rhys said, you should stay in the city. You can even look at some places llike the Holiday Inn, and some other hotels downtown.
You will have to do a search. If we weren't moving, I would have you stay here....you can get to Liberty Park in 3 minutes from our house And where we are moving to..you walk outside our condo...walk 1/2 block (not even)...and there she is! Miss. Liberty herself....all tall