Japan Oct 24 – itinerary check and suggestions required!

We are a couple in our 30s, love nature, hikes, culture and I really like cultural and artistic immersions.

Day 1 – Tokyo-  Meiji Shrine + Outer Gardens + Harajuku+  Chidorigafuchi Park + night walking tour 

Day 2 – Tokyo-  Explore locally – food / coffee shops/ museums/ experiences

Day 3 – Mt fuji and Lake Kawaguchiko on the way to kyoto – maple corridor, oishi park 

Day 4 – Kyoto – Fushimi Inari, Philosopher’s Path
 
Day 5 – Kyoto to Osaka Day trip – Osaka sightseeing and street food exploration 

Day 6 – Kyoto Sightseeing – Sannenzaka + Yasaka Pagoda Ninensaka Kyomizu-dera Temple (4-6 pm) Gion District/ Hanamikoji Street/ Gion Tatsumi Bridge/ Shirawakaminami Dori Street

Day 7 – Kyoto to Kanzawa- Explore the artisans town, kitsungi, art tour, zen garden and reach Matsumoto By night 

Day 8 – Matsumoto to kamikochi, hike and finish with onsens. Later in the day explore nagano 

Day 9 – Matsumoto to Nakasendo trail day trip, explore the old postal towns and tea houses in the area. 

Day 10 – Matsumoto to Nikko. Explore Oku Nikko Region, Ryuzu fall, Lake Chuzenji. Visiting this area primarily for the fall foliage 

Day 11 – Nikko to Oze national park – Need help with figuring out how to go from nikko to here and if there are any guided hiking tours for this region. 

Day 12 – Travel back to Tokyo, Visit Team labs, Akasaka night walk 

Day 13 – Tokyo Shopping / sightseeing
Day 14 – Tokyo shopping / sightseeing

Looking for recommendations for onsen hotels/ towns where we can possibly rent a family bath for a private experience or book a night of accommodation in any of the areas on our itinerary.
I am also thinking of swapping a day in Kyoto with one day in Kinosaki. Also another change im thinking is to do a day trip to Fuji instead of on the way to Kyoto.
I can make some changes if we find anything great. We have purchased the JR pass for 2 weeks so we will try to cover most of the regions via that, I understand that some of the bus routes like in nikko are not covered under JR. Any other recommendations to make the JR worth it?

Also I am a vegetarian, so if there are more food recommendations that can’t be missed, would love to know those.