I'd appreciate thoughts on following 10 day Japan itinerary:

1.Tokyo (arrive early evening)
2.Tokyo
3.Fuji/Hakone - Lake Ashi
4.Takayama
5.Takayama - Kyoto
6.Kyoto
7.Kyoto/Nara (Kyoto hotel)
8.Kyoto/Himeji castle (Kyoto hotel)
9.Kyoto (should this be switched to Tokyo?) (Tokyo hotel)
10.Tokyo
11.Tokyo/to airport (5:50p.m. flight)

Is this too intense? Can we do day trips to Kamakura and Nikko from Tokyo?
Someone suggested a Prince ryokan (not the hotel) near Lake Ashi - but I can't find it.