I took the Megabus to New York then took the 1 train Subway to South Ferry then took the Ferry to Staten Island (the ferry is free!) A great voyage!
You can also visit the botanical gardens, the former cottages and building of retired sailors which was a community created by the will of a gentleman called Robert Richard Randall in 1833 called Sailors Snug Harbor.
At one point one of the governors of Snug Harbor was Thomas Melville whose older brother Herman Melville visited often “perhaps attracted by a local abundance of mentally unbalanced one legged sailors ” (David Owen from the New Yorker http://www.newyorker.com/talk/2013/09/02/130902ta_talk_owen). There are no more sailors now.