Hi folks, I and my partner are planning a 13 say trip in late November and had a couple questions on order of where to visit and such.

We're currently planning on 5 full days in Tokyo broken up somehow between the beginning and end of our visit, 1 day in Hakone, 4 days in Kyoto (incl. Nara day trip), and 3 days in the Kanazawa(/Gokayama/Takayama) area. We're thinking this will give us a good mix of city, onsen town, temples, and a smaller city/town that's hopefully less crowded (due to rainy season) respectively. Questions:

1. Our tentative schedule is to do a few days in Tokyo, then Kanazawa, then Kyoto before heading back to Tokyo via Hakone, our thinking being that this will a) put Kyoto mostly on weekdays, since it seems likely to be the busiest, and b) keep Kanazawa before Kyoto since people often compare them and we'd like to do the smaller one first (feel like it will sharpen our priorities of what to see in Kyoto). Does this make sense?

2. We're also entertaining the idea of dropping one day off of one of the other locations to spend a day in Koyasan. Most likely it'd be off the northwestern leg, maybe Kyoto (if we skip Arashiyama?). We want to have a nice mix of experiences and Koyasan does seem pretty distinct and like it might be the most calming place we could go on this trip, but not sure if it's worth the extra 6ish hours of travel time we'd have to take away from something else in addition to the extra day. I know it's gotten to be a popular destination, so we wouldn't expect it to be super secluded or anything, but are the vibes singular enough for most people after all the temples elsewhere to be worth going way out of the way? Is staying at a temple feel significantly different from staying at a ryokan, aside from the vegetarian meal?

Thanks!