Tokyo to Osaka

Hi, I am planning for a 12 days trip starting from Tokyo and ending at Osaka.
Day 1-3: Explore Tokyo with day trip to Nikko
Day 4: Depart Tokyo for Hakone (using 3 days Fuji Hakone Pass)
Day 5: Hakone to Lake Kawaguchi (using 3 days Fuji Hakone Pass)

For Day 5 to 12, I am not too sure if I should go to Kyoto straight from Lake Kawaguchi and how to travel, or should I stay overnight at Takayama before travelling to Kyoto?

Any advice on where I should stay and how do I travel before flying out from Osaka?

Hi
I am Japanese but I don't know the area well, so I found official website of Shirakawa-go.
http://www.nouhibus.co.jp/english/index.html
If you plan to stay at Takayama, you can make one-day trip to Shirakawago. Otherwise, it is recommended to stay in Shirakawago.

Kyoto and Osaka is recommended place for sightseeing. But it depends what you would love to see.
If you like to see historical constructions, Himeji castle is also recommended place.