The Sound side and the Atlantic side are ten minutes apart by car and nothing alike in the water.
Nantucket Sound beaches — Oyster Pond, Cockle Cove, Ridgevale, Hardings — face south into protected, shallow water. They warm up meaningfully by late July, the surf is small, and at low tide the flats off Cockle Cove and Ridgevale run out far enough for small children to walk on. These are the family beaches and they are the ones locals send visitors to.
The Atlantic side — Chatham Light Beach, and the barrier beaches reached by boat — is the ocean. Cold water, real surf on a swell, and a current that runs hard through the breaks in the barrier. Swimming at Lighthouse Beach has been restricted at times because of that current and because of the seals and sharks offshore. Read the signs at the top of the stairs rather than the weather.
The lighthouse overlook is the best free thing in town. You park on Main Street opposite the Coast Guard station, look down over the break, and watch the whole system working: the bar, the channel, the seals, the boats threading through.
If you have one afternoon and want to swim, go to the Sound. If you have one afternoon and want to understand the Cape, go to the Atlantic side and do not get in.