Go outside and enjoy the thousands of acres of parks around the city. While New York is known for its tall buildings and urban landscape, it also has a wealth of parks--from Central Park to Coney Island and many smaller neighborhood parks in between. The recently opened Highline is an elevated park built on top of the old elevated train tracks that ran along the west side of the city. Admission to city parks is free and performances, from informal buskers to the annual Shakespeare in the Park series, occur year round. Park activities also include biking, roller skating, canoeing and swimming, depending on the amenities available at each park.
Shop for bargains, antiques or farm fresh produce. The shops along Fifth Avenue and Broadway are packed on weekends, so why not head to the flea markets and green markets instead? There are several flea markets scattered throughout the city on weekends, from Hells Kitchen to Brooklyn, not to mention the dozens of green markets that pop up in parks all over the city. Flea markets are a great place to hunt for vintage items like old records or antique furniture, while the green markets are stocked with farm fresh produce, meat, dairy and flowers, all of which is trucked down from farms that morning.
Find an off-the-beaten path museum to explore. The big names like the Museum of Modern Art, the Met and the Guggenheim will be filled with tourists on the weekends. Check out one of the smaller gems that New York has to offer, like the International Center for Photography or the Fashion Institute of Technology's Museum. Time Out New York has a great list of museums and updated information on current exhibits, as well as a list of which offer free admission. Or you can grab a copy of the New Yorker for a list of what's hot, and plan a day wandering in and out of Chelsea art galleries.