Itinerary Question

We will be in Japan April 8-16, it is our first trip to Japan. Our plan is 3 days in Tokyo, 3 days in Kyoto and we would like to experience a small town for two days in between the two. More specifically, we are searching for small town, beautiful nature, ryokan and onsen experience, and possibly hiking. We are considering a night in Karuizawa and a night in Kaga Onsen, or a night in Kanazawa and a night in Kaga Onsen or the Izu Peninsula. I very much would like to see Takayama and Shirakawago but seems the travel days would be too long for a short time. Any opinions would be greatly appreciated. Thank you.

Karuizawa is more like a Resort town. It is nice, but not a typical Japanese village.
And Kanazawa is a city. It has very nice parts though. But definitely not a village / small town.

I can�ft speak to Kaga onsen.

Your idea with Izu peninsula sounds good. Shuzenji is a nice small onsen town in the mountains:
https://www.japan-guide.com/e/e6311.html
And we�fll connected by a train.

I've visited around Kaga Onsen and the Izu Peninsula.

Izu has 3 towns which I think are appropriate to stay at. They are

(1) Shuzenji - but note that food options at night in English are very limited so it's best to get an in hotel meal.

(2) Ito - has good transport links and is big enough to have restaurants and some attractions nearby. I tend to stay at K's House which is a cheap ryokan/backpackers in an old building which is quite charming. I've got nice memories of watching the carp swim up and down the river from my room.

(3) Shuzenji - which is near probably the best hiking down south

Kaga onsen from memory is a series of small hot spring towns which are mainly reached via bus. It's very much a different feel to Izu, but the water quality is better for onsens if thats important to you.

If you go north of Tokyo into Tohoku or even Hokkaido. You'll find many small towns. And you'll still have a chance of finding cherry blossoms.

Thank you for your input. Very helpful and appreciated