[MMM]

First let me say I hope your relationship is solid. I know best friends that spent a month in Japan together, and have never spoken since. This will be a test of your relationship.

Tokyo 2-4 october.

Sounds good

4 october-12 october Kyoto (we are doing daytrips to interesting things and city around, for example Osaka)

This is long for Kyoto, and you might want to split it around Kyoto (3 days) Osaka (3 Days) and maybe a day or two in Kobe and Nara. Osaka is the central city in Kansai, and makes more sense as a central base, but Kyoto is smaller and cleaner. I just think 8 days in Kyoto is a bit much.

12 october-15 october Hiroshima and Miyajima
16-17 october Fukuoka
17-21 october Kagoshima
21-22 october Beppu
22 october Okayama
23 october Nagoya
24-31 october Tokyo (daytrips to Yokohama, Mt Fuji, Nikko)

I don't know what you are going to do for three days in Kagoshima, but maybe someone else does.