A day trip to Takayama from Kyoto

We are likely to plan a day trip to Takayama from Kyoto and return to Kyoto using our JR Pass. How do we reach Takayama? Which train should we take? Places to visit in Takayama? Which train should we take in return? Is Takayama Worth Visiting?

How do we reach Takayama? Which train should we take?

It is explained here (the train option via Nagoya at the top):
https://www.japan-guide.com/e/e5908.html?aFROM=2158_5900

Places to visit in Takayama?

Here you go:
https://www.japan-guide.com/e/e5900.html#section_spot_list

Which train should we take in return?

To have some time to actually see Takayama, I recommend to take one of the first in the morning to get there and return after 4-5pm when most places close. It gives you up to 6 hours of sightseeing.

Is Takayama Worth Visiting?

Certainly. Whether it is worth 6.5 hour train rides on a single day is a different question. If you don't mind these long trips and like a fast travel pace, then it can be worth it.

That�fs a lot of traveling to see Takayama. What is it that you want to see? The old city? The mountains?

There are several options much closer to Kyoto with similar appeals:eg
Omi Hachiman
Imaicho
Kurashiki
Miyama (a bit more difficult to reach though)

Both, the Old City and the Mountains

I read this when I got up. Re-reading, unless you are travelling for free and do not value your time - don't. I like Takayama a lot, but as a day trip from Kyoto - no. There are a ton of things in/around Kyoto to keep me busy for a week easily without doing a huge trek into the mountains. As an over-night(or two), sure thing, especially if part of onward travel. but as a there and back again in a day, seriously reconsider.