The experience of Stuyvesant Town may not be directly on point regarding plans for Atlantic Yards, but given that Forest City Ratner has long promised (as in this October 2004 flier) "new open space for the entire Brooklyn community to enjoy," it's worth noting that making space accessible may come with tensions.
(Forest City originally promised six acres; now the promise is eight acres, but not until the entire project is completed, and that could take 25 years.)
The Stuy Town story
The New York Times reported 12/11/11, in Skating Rink Spurs Residents’ Latest Fight With Management:
In the eyes of some longtime residents of Stuyvesant Town in Manhattan, the ruin of their apartment complex has come in stages. First, the development’s managers opened a green market last summer, which drew large crowds of nonresidents, and they scheduled noisy music concerts afterward. Then they allowed vendor carts onto the property: neon-colored trucks that sell tacos, Greek food and desserts on the tree-shaded paths.
...Now, a seasonal ice-skating rink that opened at the end of November has again put management and many residents on a collision course.
A number of residents view the rink as another amenity that the property manager, Rose Associates, is using to try to lure new tenants who are willing to pay higher rents and who have no sense of the role the complex has played in providing low-cost housing to middle-class residents.
Some who live near the rink, which also has a cafe, complain about noise and music and the $7 fee to skate.
...Rose Associates, which manages the apartments for CW Capital, a group of lenders that took over Stuyvesant Town and the neighboring Peter Cooper Village in 2010, said it would provide residents free use of the rink for a few hours on Wednesday afternoons and Sunday mornings. The rink, which was erected over a playground, is open 3 p.m. to 9 p.m. weekdays and 10 a.m. to 9 p.m. on weekends and school holidays.
...[Council Member Dan] Garodnick has sent several letters to the city’s Department of Buildings, Department of City Planning and Department of Environmental Protection to find out if a pay-for-use rink can be placed within a residential zone and if the electrical wires and noise comply with city codes. The Department of Buildings found that the rink was legal but cited noise concerns. In response, Rose Associates put sound buffers on the machinery and agreed to end the music by 7 p.m.