B.M.
The Transit museum in Brooklyn. One stop from Manhattan, the kids can drive an nyc bus and they have real trolly cars from all time periods to sit in and look around. It is housed in a real (but no longer used) subway station.
Dylan's candy bar-- overpriced, but right across from Bloomingdales. It is like going into Willy Wonka's factory. This is a good companion to a stroll in southern Central park.
Take the Staten Island Ferry, then just turn around and go back. It is a free harbour cruise. Then you are near Battery park and the stock exchange etc.
Water Taxi-- Goes from Carl Shurz park in the East 90's around the tip of Manhattan and ends at the Chelsea Piers where there are lots of kid-friendly and family friendly activities. the Taxi has several stops along the way. Check on the web for times and locations. This is great fun, not too expensive, and brings you to cool places.
Don't bother with The Children's Museum-- it is not so great, but If you are on the West side of Central park, of course the natural history museum is always good-especially if it rains and your children need to run a bit.
The 10 year old (and adults) might enjoy the Lower East-Side Tenement Museum. Housed in a real tenement. tours only, but great.
And finally (but not exhaustively) the Museum of the City of New York if you want to find out more about how the city came about.
I hope this helps. Have a great time!