Well, you said you're going to Hiroshima and working back, so I'm going to assume you're not going to Kyuushuu. Also I'm going to skip shit like Osaka, Kobe, Kyoto because those are so touristy that you should know whether or not you want anything to do with them. That's why my above suggestions definitely include going to Kagawa for Takamatsu, Sanuki, or Marugame, or Tokushima for Iya, Tokushima City, and Naruto. If you go the Okayama route, Okayama city is quirky but nothing too amazing. If you go a more northern route, you could do Tottori City for the dunes, but you're going during November so the usual summer parties and shit will have ended. If you get down to Wakayama, you'll be treated to a bunch of amusement/water/safari parks and you can check out Shirahama too.
I'm not going to go into detail about central Japan like Gifu or Aichi or Gunma because more than likely you won't go to any of them lol. I'd say pick whether you want to stay on Honshu or go down to "real" Japan on Shikoku, and then plan accordingly.