When sailing out of the Brooklyn Cruise Terminal one of our favorite treats is going to the top deck of the Queen Mary 2 and watch the ship go under the Bridge. I don't know how tall the Princess ships are, the QM2 just misses the bridge be a few feet, it is really a strange sensation thinking it will hit the bridge.
Either way, I think it is worth while to go to the top deck for the sail awy
You can see the Statue of Liberty while still in port, and yes you can see the Statue while sailing away.