Madaket, on the far west coast, is one of the island's most beautiful beaches. The neighborhood offers a relaxed, family-friendly vibe and was once home to Mr. Rodgers. It's especially beautiful in the evenings, when locals and visitors gather to watch the spectacular sunsets.
Consider riding a bike out there, although you can also drive. Young's Bicycle Shop is the time-honored spot for renting cruisers and Bianchis. After walking the bike over the cobblestones in town (don't try to ride over them!), ride down the Madaket Road Path for six miles until you reach the Atlantic ocean. Once you're out there, grab some tacos from the take-out counter at Madaket Millie's and hit the beach. If you stay for the sunset (or are too tired to ride back), you can hop on Nantucket's bus service back to town with your bike.