Nantucket is a perennial favorite among Indagare travelers, and it’s easy to see why. Off the southern coast of Cape Cod, this 14-mile-long island has preserved a sense of place that few American destinations can match—cobblestone streets are lined with gray-shingled houses, wild rose hedges spill over white picket fences and the harbor still looks much as it did in its whaling heyday. The appeal is equal parts nostalgia and polish: days unfold at the beach with a lobster roll in hand, strolling...