This space would be good for a football or frisbee game, except for two things. First, the area is fenced off. Second, in a very large gravel circle in the middle of the quadrangle is buried a large cannon. This is very puzzling. The Orange Key Tour webpage says that the cannon was used in the Revolutionary War, and in the War of 1812.
Classes paint their years on the cannon in the fall, and hold football pre-game bonfires here.
None of this explains why the cannon is in the ground. The story I heard was that Rutgers students used to steal the cannon, and so it was buried to prevent pranks. Then I found a somewhat more plausible story on the web. The cannon was used as a decoration after the revolution, but was taken to New Brunswick for defense in the War of 1812. Princeton lobbied unsuccessfully for years to get the cannon back.