Oh, yeah, I'm *SO* glad someone suggested that for the Statue. It's phenomenally faster. I did it once, and it was amazing! Big long line to buy tickets; absolutely nobody in the "already ticketed" line. I didn't even have to go to "will call"; I printed mine out at home, and we walked straight up to security.
Also, if you can get up and out early, go to the Statue early--all the other tourists won't be there yet. And I'd suggest just the Statue, if time is tight. Or, maybe see the statue from the boat, and then get off at Ellis.
My other "NY Harbor" thought: If you can at all get out on the water, DO!
Then look around and imagine what that huge sheltered harbor must have looked like to the folks just settling from Europe with their sailing ships and use of natural resources. Imagine the buildings not there, and hills with trees as far as you can see. And imagine that huge landmass looming to the west and north, with all its natural resources to ship back to poor depleted Europe (lumber, furs, animals to hunt and trap, land to grow crops on...) just a short, direct oceans-breadth away.
And see why the city became the mega-city that it did. See how shipping mattered so much. It's fascinating. (Plus it's cool to see the city from the water--see if you can get the Barney Miller view.)