Central Park and the CP Zoo are great to explore. I think you will need to reserve for Statue of Liberty. You can do the 9/11 Museum and Freedom Tower the same day. Just see the memorial fountains if you don't feel its age appropriate for your kids. Nice along Battery Park, too. Other "free" things to do is just pick a neighborhood to explore, Chelsea and along the Highline or Soho or Upper West Side. I don't go into the city often anymore, but we always take the subway. Its quicker and I imagine mosly cheaper unless you are going a short distance.