Believe it or not, New Yorkers are active sportsmen, and they have more athletic facilities at their disposal than most other city dwellers.
In Central Park you can rent and ride (no cars allowed on weekends) bicycles, hire a boat or even a horse. To play tennis on the city courts you need to buy a season permit, but there are also private indoor and outdoor courts (see the Yellow Pages of the telephone directory) for rent by the hour. Otherwise, you can just follow the example of the thousands of New Yorkers who jog around the reservoir and along the city sidewalks.
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In winter there is skating in Central Park (at the Wollman Memorial Rink) and at Rockefeller Center.
New York boasts 18 miles of public beaches with mostly clean if sometimes chilly water. The best, Jones Beach just beyond the city limits on Long Island, is a good 6 miles long.