I would not go up the statue of liberty.

It is cramped, basically a nightmare. Endless spiral staircase, queues near the top aswell.

Not only that it moves.

And the view at the top is dreadful.

It is a great photo opportunity at the bottom on the outside though.

Other than that I'd recomment Katz deli (have pastrami on rye, everything else was a bit "meh".)

And ice skating in central park.