Cycling is the best way to get around Nantucket. The island is flat, the distances are manageable, and there is an excellent network of dedicated bike paths connecting the town centre to the main beaches and to the village of 'Sconset. Bike rentals are available from multiple shops within a block of the ferry terminal. A good-quality hybrid or cruiser can be rented by the hour or by the day.
The island has a public bus service (the NRTA shuttle) running routes to the main beaches, the airport, and 'Sconset during the summer months. Taxis and rideshare are available but not always quick in peak season. A small number of visitors rent cars or bring their own, but parking in town is limited and the distances don't really justify it for most trips.
Walking is perfectly adequate for the town centre itself — the historic district is compact and almost everything on Main Street and the wharves is within ten minutes on foot.