With your late arrival, you made a good choice for your hotel. It would be a hassle to get into the city and check into a hotel at that hour.
My only advice is to treat yourself to a taxi or van service to minimize your travel time into the city, but check with your hotel for the quickest way to get there. We took the bus once on a friends advice to Newark and it was a hours-long ordeal. You don't want to spend your limited time in the city just trying to get there.
The good thing about the New York port is it is located near mid-town on the west side, so your daughters will have some time to shop some before you leave.
Your daughters will probably enjoy shopping in both Hamilton and St Georges.
The ship will have good activities while at sea also. We enjoyed the pool in the afternoons or watching the movie in the show lounge. We had a late night party in Hamilton (Wednesday night I think) on the pool deck. The staff is very attentive and you should have good service all around.
Enjoy your cruise.