Going to New York soon, got a few questions

[Socko]

First of all, can't wait to see the city. Coming from a small country where highrise buildings rarely top 500 feet. I'm so hyped to see all the skyscrapers up close.

We will be staying on Manhattan.
I already checked for Best Buy and Target locations for to get me some more movies

The only paid visits that I've booked so far are the Empire State Building and the Statue of Liberty and I've a question about the latter.
My dream was always to go into the crown. Never realized you have to book way in advance to get in there.
So I was going to settle for just the pedestal. The weird thing is, if you want to take the ferry from Manhattan it's sold out at the time I want to go, but the New Jersey side still has tickets. Both ferries arrive at the Statue of Liberty. Why would it matter where you come from?

Anyway, here comes the question:
What is the quickest way to get from Manhattan to ferry of New Jersey?
I reckon a taxi since the public transport makes me walk 35 minutes afterwards.
Yellow cab and Uber will get me there where Uber is the more expensive option.

And if you guys have any tips of what to visit I'm all ears.