All four of my grandparents came to the US through the port of New York. My mother's parents entered via Ellis Island (as far as I know), but not my father's.

My great-uncle (father's father's older brother) was the first of the clan to make the move, and he saw people turned away at Ellis Island because of apparently minor illnesses. This frightened him, and so he instructed the rest of the family to avoid taking this chance by saving up for second-class fare (as opposed to third-class, also known as "steerage").

A second- (or, of course, first-) class ticket allowed you to stay on the ship when it stopped at Ellis Island to offload most of the immigrant passengers (those in steerage). You then entered the country via the regular terminal on the Hudson River in Manhattan, where customs/immigration was much more lenient.

I was able to visit Ellis Island about 12-15 years ago, shortly after it had been rehabilitated. Our kids were still young, and strongly impressed. Definitely worth the trip; the link above to the National Park web page probably provides as much info as I could.

The island is *very* close to Bedloes Island, site of the Statue of Liberty, and the ferry services allow you to visit either or both islands, coming either from the tip of Manhattan (Battery Park) or from Jersey City (Liberty State Park). The islands are actually *much* closer to the New Jersey ferry launch, which in turn is very convenient to the Turnpike. So, if you're not already in The City, it's easier/quicker/more convenient to approach Ellis Island and the Statue from NJ than from NY.

On the other hand, if you're already in NYC anyway, the longish voyage from the Battery is a nice tour of the harbor (especially in nice summer weather).