Please help divide my time

I will have 2 full weeks in Japan late September (not counting arrival/departure from Narita), and I am thinking of making 2 "bases" - one in Tokyo and another in Kyoto - from which to make day trips.
We dislike checking in/checking out, packing/unpacking, but! for one of us Naoshima Island is a "must", so we have to add an overnight stay there as well.

Now - what would be the best way to divide the time between Tokyo and Kyoto (how many nights in each)? And where should we add the night at Naoshima island?

I was thinking maybe 6 nights in Tokyo (+ day trips), then take a train (+ another train + ferry) to Naoshima, spend the night there, then - on to Kyoto, spend the remaining 6 nights there (in the city + day trips), then take the bullet train back to Narita for departure (our flight is late afternoon).

Does it sound reasonable? Or would one city (+ day trips) require more time than the other? Also - should we add Naoshima at the end of Kyoto stay instead of in between Tokyo and Kyoto?

Thank you!!!