I lived in Japan for a few years, and actually just helped a friend plan their trip which they just got back from. They had a similar length trip and in the Kansai region they really enjoyed Kobe and Nara. I have a personal bias for Osaka as I have family there and as Im sure you know from your research good spots there to hit are USJ, the aquarium and dotonbori
If I had to recommend an activity outside of Osaka, it would have to be Nagashima spa land. Despite its waterpark being closed this time of the year, you get a very nice Onsen experience if you book one of the park hotels. And the rollercoasters there are insanely fun.