If you want to cool off like a local -- and aren't a germophone -- take a dip in one of the city's 54 public outdoor swimming pools. They're free and open each day from 11am to 7pm. If you want to stick around before or after your swim, you'll probably be close to a handball court, playground, or at least a nice bench in the shade. Bring sunscreen!
Yes, there are excellent beaches not far from the city and I don't mean the Hamptons. July/August is very hot and following the locals is a good idea. Long Beach is a pretty town by the sea with a long boardwalk, good swimming and surfing (non-residents pay $6 entry), and Jones Beach State Park ($8 parks entry fee) has 6 miles of seafront, 2 bathhouses and tons of amenities (but bring your own food).
Both feature white dune sand, blazing sun (remember the sunblock!) and safe swimming with lifeguards during the summer.
Long Beach: Catch the Long Island Rail Road (LIRR) from Penn Station to Long Beach, then walk to boardwalk;
Jones Beach: Catch the LIRR (Babylon branch) to Freeport, a special bus service, or drive
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