After decades of being off-limits (for use by the Coast Guard), Governors Island is now a big public park with beautiful scenery, historic buildings, amazing views and areas for art exhibitions. Word hasn't spread yet so the Island is vastly under-utilized. You get there by a short ferry ride from southern Manhattan or Brooklyn.
The Island closes during the Winter. This week it's opening for Summer with a whole bunch of art exhibits and performances. I'm heading there today. Ferry rides are free this week!
Here are some pics from my last visit.