First timers to Japan

Hello,
We are heading over to Japan for the first time in April and as this is a busy time we are wanting to finalise our itinerary to start booking accommodation. We don't like shopping and prefer spending our days sightseeing, walking around and sampling local cuisine. We are interested in the 'old' japan, and don't want to spend too much time in the bigger cities.

We will have a 14 day JR pass. Is the below itinerary too ambitious? Would you suggest spending less time or longer time in some places?

10th - arrive in Tokyo at 6pm - stay close to airport
11th - early start. Activate 14 day pass and travel into Shinjuku.
12th - Tokyo
13th - day trip to see Mt Fuji
14th - Shinjuku to Kanazawa. Early start
15th - Kanazawa
16th - Kanazawa to Shirakawa-Go to Takayama
17th - Takayama
18th - Takayama to Kyoto. Early start
19th - Kyoto
20th - Kyoto
21st - Kyoto day trip to Arashiyama
22nd - early start. Kyoto to Hiroshima to Osaka (late afternoon)
23rd - Osaka
24th - Osaka to Narita airport 8pm flight

I am debating on the Osaka part of the trip. Friends recommended it as they enjoyed it better than Tokyo, but as we are not really that interested in modern cities maybe we should extend our time somewhere else?

Thank you for your input!