Wake up as early as you can, for example at 7 am.D Don’t loss time sitting for the breakfast, take a baggel and a coffee in some street food post instead and eat/drink them while you’re already in the Metro. I beg every Newyorker does it in its routine.
Take a metro to South Ferry metro station, the southern most part of the city. From there, you can take the Free Ferry to the Staten Island. That way you’ll able to see the Statue of Liberty from the Hudson River. If you wanna step your foot into the Statue then you’ll have to pay another transport, but for me seeing it from the boat was enough.
After the ferry trip I recommend you to walk towards Wall Street, the world most relevant financial district. You’ll have the chance of seeing and touching the Bull balls for good luck, and why not, eat a “burrito” while seeing its fancy dressed people walking around.