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.