13.5 Days in Japan (Osaka → Kyoto → Mt. Fuji → Tokyo) – How to split my time?

Hey hey! First post here.

I'm heading to Japan in mid-October – flying in to Osaka and flying out from Tokyo – and I'll have about 13.5 days on the ground. I'm still figuring out how to split my time and could use some advice.

My rough plan is:
– Start in Osaka (probably a hotel to fight jet lag)
– Then head to Kyoto
– Make my way to the Mt. Fuji area (planning one night in a ryokan)
– End in Tokyo

I'll be traveling with just a backpack, and for most of the trip I want to stay in capsule hotels. I'm also totally open to day trips to smaller cities along the way – just not sure which ones are worth it or how to balance everything. I'd like to have a nice mix of city/nature.

So, how many days would you suggest for each spot? And any favorite neighborhoods or areas to base myself in?

Thanks in advance!