Summary of editorial
Here, adjacent to Whitey Ford Field in Astoria, is a good set of equipment you can do pull-ups, dips, and core exercises with. It's right along the waterfront and has a beautiful view of Manhattan; however it's a bit far to get to unless you live nearby. There is no train station nearby, so that means to get here you'd have to take a bus from the train station or walk quite a bit.
Photo: MR Calisthenics