Aogashima is one of the Izu island of Japan that isn't very famous for some reason, but definitely should be.
The whole island is basically a volcano rising steeply up out of the sea. Within the caldera of the volcano is a second smaller volcano with its own second caldera!
The island has a population of about 200 living in the village inside the large crater.
But I can't find a lot of information about tourism there. Wikivoyage has a brief article. What I can't find is whether it's possible/safe to visit the inner crater/caldera.