Quick Question for New York Readers

We are planning on going into the city tomorrow and I have NO idea how to do this.  Seriously, I don't even know where to begin.  Any and all advice would be greatly appreciated.  We only have tomorrow to see the sights the kids are interested in(Time Square, Central Park,Statue of Liberty) so I'm wondering if we should use the train system and walk or if we should pay for a red bus tour.  If its doable I'd rather the freedom of being on our own time schedule.  The only thing I know we are doing for sure is not attempting to drive into the city.  We are catching the train and taking a 2 hour trip into the city which will take us into Grand Central Station.  From there we are WIDE open to opportunity and experience.  Any help or suggestions?

I'll share a little about Ash this evening when I have a moment to sit still and compose a few thoughts.  Thanks for your help.