Keep in mind that Kansai International (KIX) is out of service with severe damage from the latest typhoon. I haven't seen recent estimates for repairs but they may or may not have it back in service by 10/1. That might impact your plans.
Of places easily reachable from Osaka/Kyoto, I like Hiroshima + Okayama + Kurashiki. From there, you could fly from ITM or take the shinkansen back to Tokyo for departure. Another option might be Shikoku island.
If those don't appeal, I also like Kyushu. The long shinkansen ride to Hakata (Fukuoka) plus the Limited Express from Hakata to Nagasaki would be a long day of travel but a couple of days in Nagasaki would make it worth it. Add a couple of days in and around Fukuoka and then a flight from FUK back to NRT or HND for departure would fill your time.
I would want a least a full week for Hokkaido.