The Vineyard's biggest, most popular public beach.. In Short Also known as Katama Beach, this three-mile barrier beach along Norton Point is among the most crowded on the island. At one end, strong surf comes with occasional riptides. For calmer waters, walk down the beach to Katama Bay. If you keep walking, you'll eventually walk right onto Chappaquiddick: Over time, sand has built up and now connects the island to the mainland.