Depending on where you stay and how active you are will decide whether you will want to rent a car, bicycle or take a bus and walk. Be sure to check your accommodations location and access to town, beaches, hot springs, etc. etc.

Hachijo's undulating roads make for lots of interesting mountain biking adventures and you are never far from a place to swim.
You can bring your own bicycle whether you boat or fly.
Both services have surcharges for bicycles.
If that's too strenuous you can always rent a scooter or a car for the day. Cars from ¥3,000 per day, scooters from ¥4000.

Be sure to bring an International Drivers License!!