For free - Visit the Public Library on 5th Avenue and see the original Winnie the Pooh toys, about who the books were written.
Staten Island Ferry for views of the Statue of Liberty.
Theodore Roosevelt's House - lovely period house, great if your older kids like history
Times Square - lights, Toys R Us, M&M shop, Hersheys shop
Walk (or scooter!) the Brooklyn Bridge - catch the subway to Brooklyn, get pizza at Grimaldris or icecream at Fulton Street then walk back for great city views
The Highline
The Apple Store
Central Park
Federal Reserve - small museum/information centre, then a trip into the vault to view the gold ! It's free, but you need to prebook.
The New York Fire Department Museum wasn't free, but it was quite cheap. They got us all dressed up in a firemans outfit, and we got to hold the hose, and we didn't even have the kids with us ! 
Window shopping on 5th Avenue.
Trump Tower - although I don't know if you can go in there anymore.
If you are planning on visiting a lot of the major attractions, look at getting a New York Pass or City Pass to save some money and skip queues.