I am a refugee from the east coast, and will do my best to start an answer.
For Ellis Island and the Statue of Liberty, your hang up will be the tour boat schedule. I don't know what they are doing these days.
If by the Met, you do mean the Metropolitan Museum of Art. Well, that is a day killer all by itself and then you have to walk fast. Times Square, unless you want to look in all the souvenir shops is about 15 minutes and most of that will be dodging the panhandlers.
Liberty Harbor is closer, and convenient to a cross-river transportation. There is also an RV park up river that is close to the railroad.
Good Luck
Matt