Chappaquiddick — "Chappy" to locals — is the much quieter island reached by a two-minute crossing on a small flat-deck ferry called On Time from the foot of Edgartown's Daggett Street. There is no town and not much commerce; what there is is good beach, big nature reserves (Wasque, Cape Poge), and a couple of small sights including the Mytoi Japanese-style garden.
The Cape Poge Lighthouse at the north-east corner is reachable only by four-wheel-drive on the sand, on a guided tour from the Trustees of Reservations. Bring water, sunscreen, and your own bicycle if you want to cover any distance.