Planning a trip to Manhattan, NY. What is there to do?

Im planning a trip to NY and will be staying in Manhattan. I cant really think of too much to do except for go to times square or on top of the empire state building. I work at a museum and really don't want to go to one when I get to New York. I would like to definitely visit the landmarks like The Statue of Liberty. I would also like to visit Brooklyn, Harlem, Queens, The Bronx etc.