Hachijōjima (八丈島) is an island in Tokyo prefecture, some 300 kilometers south of Tokyo city.
Tokaikisen  operates a daily overnight ferry from Tokyo's Takeshiba pier, near the Daimon metro station. Leaving Tokyo at 22.30, and arriving 9.30 - prices vary seasonally but expect to pay around ¥9000 for a reclining seat.
ANA (All Nippon Airways) flies between Haneda airport in Tokyo and Hachijōjima up to four times a day. Prices vary seasonally, but expect to pay around ¥25-30,000 return. You can get around this by booking on the english version of the Japanese site. From this you will have access to the lowest fares.
Most hotels have bikes for hire, and there are several rent a car agencies on the island.
Hunt for for glow in the dark mushrooms, diving, snorkeling, and trekking to secret waterfalls in the mountains.