[samurai007]

I notice you spend part of 3 days in Takayama and then head to Hakone. IMO, it's better to go Takayama -> Kamikochi (Japan Alps) -> Matsumoto, then spend the next morning seeing Matsumoto Castle before heading to Hakone. Hiking in the Alps and seeing one of the best castles in Japan (the best IMO now that Himeji is being renovated) is worth it.