@Eva,
Eva, Even if the Statue of Liberty was open, you wouldn't need to go there. You ain't gonna walk up a narrow spiral staircase. However, the statue is worth seeing. Just take the ferry to Staten Island. You'll see Miss Liberty from the water--the best view, IMO. Sorry about Ellis Island.
I haven't been to the theater in a very long time. Prices are high. But the experience is wonderful. I hope you get to see something you'll both enjoy.
I suggest you plan ahead with the Metropolitan. It's enormous. My favorites: the Rembrandt and other Dutch masters section, the impressionists, and the Egyptian wing. They've reconstructed a tomb right there in the museum.
I highly recommend the Frick, not just for the art, but for the place itself. A former manstion of a very rich person. Stunning to see. It has my favorite Rembrandt, two Vermeers to knock you socks off, and two Turners that set the water on fire.
The Museum of Natural History is one of my favorite places in the city. It's gigantic beyond big. One of the largest museums in the world. You might want to check out what the current special exhibit is.
It would be nice if you could do some strolling downtown (Wall Street, China Town, Little Italy, east and west villages). It's a different city down there. Built early. Small narrow, nonparallel streets.
Gonna stut up again.