Ellis Island

From 1892 until 1954, Ellis Island was the main point of entry into the U.S. for immigrants arriving from Europe. This was the first stop for over 12 million people trying to make the U.S. their home. The island itself is a tiny-ish thing, mostly covered with buildings of which only one is normally open to the public. (There are a slew of other buildings, mostly medical buildings according to Wikipedia, that aren't open but appear to be under renovation.) To reach the island, you take the same ferry as to reach the Statue of Liberty. Liberty Island is the first stop; Ellis Island the second; then the ferry returns to Battery Park. There's also a ferry leaving from the NJ side.

If you go, I recommend coughing up the $8 for the audio tour. It's well done and will free you from reading each exhibit sign, allowing you to spend your time taking in the atmosphere and letting your imagination wander.