If you do take a train somewhere there is a trasportation museum annex in Grand Central (by the way Grand Central is a tourist attraction in itself. So many movies have been filmed there in a it is historic. Anyway, in the museum you will learn about the subway, over 100 years old now, how they dug they tunnels, that NYC had the first express lines, and other interesting stuff. They have really cute souvenirs. The main museum is in Brooklyn if I remember correctly http://www.mta.info/mta/museum/ but the annex is a neat way to just spend a half while at Grand Central.
I thought of more food. Famous deli’s like Carnagie or Stage. I think Katz’s deli is where Meg Ryan had her fake orgasm in Where Harry Met Sally.
You can take the PATH train to Jersey CIty or Hoboken and walk around. http://www.panynj.gov/path/