The vast lawn of Manhattan's Central Park is widely considered by Manhattanites to be their personal land grant; you'll find frisbee players, picnickers and all sorts of activities taking place here that you'd find on any private lawn in America. The difference is that here you'll be amazed at how good people are at ignoring each other's activities—until you're bonked with a frisbee or someone's dog (forbidden in any case from the Great Lawn) trots over to your sniff your food.
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