+1 on the Greenway. You can rent bikes from
Bike N Roll at several locations on the Greenway and then follow that around Manhattan. You can go up, past Midtown, the Intrepid Air & Space Museum, through Riverside Park up to the George Washington Bridge and Little Red Lighthouse, all the way to the Cloisters and the northern tip of Manhattan.
Or you can take it south, past the Village, the World Trade Center, Battery Park City, South Ferry where you can catch the boat the Statue of Liberty or the Staten Island Ferry. From there you can go up the east side portion, past the South Street Seaport, Brooklyn Bridge, and eventually to the U.N. Cycling on the Greenway is a great way to take in many of the sights in Manhattan and much of it's traffic free.