I don't know that I would advise taking the ferry to Liberty Island. We did it a few weeks ago and even in the slow season it was a long slow process, including long waits in line and two very thorough security checks which include x-ray machines and chemical sniffing chambers, removing shoes, putting backpacks in lockers, etc. For children that age, just take the Staten Island ferry and enjoy the view of Liberty from the boat.
We also visited the American Girl Place. The 9 yr olds loved it, but I wouldn't do it unless your daughter was a fan. It can be overwhelming, and it's really just a giant store, geared to getting you to buy stuff. The show the previous poster mentioned does not allow children under the age of 6 in. Just as well - though well done there were some intense moments that even my 9 year old found a little disturbing (e.g. Addy and her mother escaping from slavery, being chased by hounds, nearly drowning in the river, etc).
OTOH, we loved the Museum of Natural History. Lots to see and do for children and adults. It's quite large, though, so don't feel the need to see it all.
On past trips we've gone up to the top of the Empire State Building, but again, we spent much time in long, hot lines and it was quite crowded at the top. I hear the Top of the Rock(effeler Center) is a more pleasant experience.
I second Central Park, see the zoo there, or go over to the Bronx Zoo which is supposed to be great.
NYC is exciting and vibrant. Enjoy your trip, whatever activities you decide on!
-Corinne