As has been mentioned, I would recommend the hop on hop off buses. You can get 24, 48 or 72 hour passes, and some include a night tour. When I got mine in Feb, it included free entry to Empire State Building (another must), a free river cruise and some other things I paid no attention to! We got on and off at most attractions, spent some time wherever and then got back on.
The Staten Island ferry is a good way to get a free and different view of the skyline and of the Statue of Liberty.
For the same reason, I would also recommend a helicopter ride.
I also enjoyed the walk from Brooklyn, over the bridge back in to Manhattan.