I can give you a rough idea.
Day One: Manhattan, focusing on midtown and the museums
Day Two: Manhattan, focusing on the Financial District and the waterfront
Day Three: Brooklyn, focusing on Coney Island and the museums
Day Four: Queens, with a stop at the Museum of the Moving Image
Day Five: The Bronx, focusing on the Bronx Zoo
Day Six: Staten Island, focusing on the Richmondtown Restoration and the zoo
That's an awful lot to do, but if you were determined, and with a good guide book with you, you could in theory do it all in six days.