Kozushima is a small island in the Izu chain of islands south of Tokyo. My favorite way to get there is a night ferry from Hamamatsucho. It departs around ten PM and you get to spend the evening suspended in the infinite blackness that is the middle of the ocean in the dead of night.
Wikipedia on the island:
Kōzushima is 18.87 km² and has a population of approximately 1,900. The island forms part of the Fuji-Hakone-Izu National Park. The island is accessible by ferry from mainland Tokyo, Shimoda, Shizuoka, or other islands. There are also daily flights on a 10-seater turbo prop plane from Chōfu Airport, in western Tokyo.
It has many hiking courses around its volcano, Tenjō-san, which dominates the island and is also a great place for diving. Its white sandy beaches make it an excellent place to swim in summer, since it receives considerably fewer visitors than the other islands in the chain. Winter visits are discouraged, as you are likely to get stranded on the island due to bad weather.