Years--no, decades--before Long Island City became a happening neighborhood, Socrates Sculpture Park was there, staking a claim on a patch of land that had been abandoned and turned into an illegal landfill. Since then, the park has become a cultural hub of the neighborhood, hosting year-round outdoor exhibits of contemporary sculpture. During warmer months, it also has a full calendar of events, most of which are free, including yoga and capoeira classes, international movie screenings, and art-making workshops. The park is also a launch point for kayaking (also free!) during the summer.
Note that the Noguchi Museum is right across the street; along with Socrates, it makes for a inspiring art-centered outing in this increasingly popular Queens neighborhood.