In the winter hte park/island isn't worth more than 45 minutes but as others suggested you can get a wonderful view from Liberty Science Park which is likely more entertaining to the kids anyway as the ferry ride in December won't be ideal unless it is symbolic for you to see/touch it.

It will cost a pretty penny from EWR airport to Jersey City and bit cheaper on the return. http://www.panynj.gov/airports/ewr-t...n-service.html

You can save a little cost renting a car for 1/2 the day if you wish to stop for lunch somewhere. However, don't know estimate rental car during Christmas break/holiday. Or you can Uber/Lfyt.