The mytical island
Once called Welfare Island, Roosevelt Island is the almost mythical island between Queens and Manhattan, associated with a whole host of rumors: Dogs ARE allowed there, the Tram is pretty fun, it’s not haunted (though remnants of the Lunatic Asylum still stand on the island’s south end), and it is indeed a part of Manhattan. Though small, the area offers expansive green space and affordable rents.
The 4 minute ride, which offers spectacular views to its passengers, has been praised in the New York Times as "the most exciting view in New York City!" It costs a mere $2.25 each way ($4 for a round trip).
At its peak it climbs to 250 feet above the East River. Two cabins make the run every fifteen minutes from 6:00am to 2:30am (3:30am on weekends) and continuously during rush hours.
You can visit neighboring Southpoint Park, Its wide walkways pass wildflower-covered mounds where remnants of old buildings lie. Towards the south point, the ruins of the weed-covered smallpox hospital look like a medieval castle, abandoned for far longer than its mid 19th-century birthday. It's interesting to see what will come of the area. And the views are nice. From the tram, it's a 10-minute walk south.
North Point Lighthouse
Once there you'll reach a lonely Gothic-revival lighthouse, built in 1872 by the city to help light a nearby insane asylum. The asylum's gone, but there's some shady lawns and sitting spots by the lighthouse that look north towards Randall's Island as if you situated plump in the middle of the East River. In all, a very unique vantage point in New York.