LIBERTY, ELLIS & STATEN ISLAND
Liberty and Ellis need no explanation, but Staten Island is considered an afterthought.  The Statue of Liberty is closed, so I would suggest taking pictures while on the Staten Island Ferry instead.
Ellis Island Immigration Office.  Now a museum with an inesthetic steel structure outside.  If you have a distant relative that landed here, you can check government archives for a fee.  Or else, you can check the Internet at www.ellisrecords.org
The Statue of Liberty.  Closed, so don't take the ferry unless you want to visit Ellis Island!
Garibaldi-Meucci house on Staten Island.  The house was moved, but in this house the telephone was invented by Antonio Meucci before Bell stole the patent from him, and Giuseppe Garibaldi lived in exile here while he disputed with the kings on how to form the Italian government after it was formed.  And you thought Staten Island had no history, eh?