Do you know any cruise lines who travel around some of the Japanese islands?

Traveling would be having an itinerary that would have the boat stop at some of the islands and let us explore or something like that.

The US navy.

Try this site..www.viator.com/tokyo-cruises
..you have to wait for 5 sec before the homepage appear then just select the country (Japan)..

Domestic regular cruising is not popular in Japan except ferry service between main islands. Traveler uses airflight which save time and money efficiently much more.

If you really want to go travel to Izu Islands or Ryukyu Islands etc by sea., some limited service may be available.

http://www.asahi-net.or.jp/~aa5k-ysd/funatabi/000000tklink.htm
(sorry but Japanese text only)

yes. go to JTB and follow their lead.