Everyone has to ride the Staten Island Ferry. It's free, the view is great, and you can drink beer on board. Or, if you're up for a longer trip, take the MTA ferry to Sunset Park or the Rockaways for $2. Check the schedule beforehand, since those ferries run only a few times a day during the week.
Bayonne Bridge One of the longest steel arch bridges in the world, the Bayonne Bridge spans the Kill Van Kull to link Bayonne, New Jersey, with the Port Richmond area of Staten Island, New York. It is one of the most spectacular bridges in the metropolitan area, with a mid-span clearance of 150 feet that permits ocean-going vessels to use this entrance to Port Newark and the Elizabeth-Port Authority Marine Terminal without interference.