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I'd wait for the next off period of school that includes time to spend 4 days there outside of your travel time. As it is, you'll have barely two days to see NYC.
Can you possibly fly? Sometimes you find flights/hotel deals...
Ride the subway in order to get around Manhattan, but make sure to ride after people get to work, and don't ride around 5 pm. The crowds are astonishing. Don't ride after 8 pm. Don't carry a pocketbook. Have a travel strap bag that fits around your torso around one shoulder and wear a jacket over it so that it's not seen or easily accessed by a pick-pocket.
If you want to go to a Broadway play, go to Tickets in Time Square and stand in line to get half priced tickets . I think around 1:00 in the afternoon is when they sell them. Be flexible in what you will be willing to see, and you can get a deal.
My kids dearly loved the Museum of National History and the Central Park Zoo. FAO Schwartz is quite wonderful. I'm sure your girls would love American Girl (I had boys, so we never went to that...)
Make sure you have some bandaids in your bag in case of blisters, and wear comfortable shoes. Teach your girls to use their eyes and ears and act with confidence so that they don't stand out as a potential victim. That's always what I did, and the most trouble we had was a homeless man kicking my husband. It seems a shame to have to add that to the "itinerary" of going to a large city, but it's smart to do it, and should be part of the education you are trying to provide.
Have a great time!