Combining Koyasan, Ryujin & Nachi Taisha?

we will be going on a 3 week trip through Japan
Apart from the highlights like Kyoto and Tokyo I would like to include some off the beaten path locations in beautifu scenery to get a more zen experience of Japan than just busy cities

I would like to go to Koyasan, stay for 1 night and then maybe stay a night in Ryujin Onsen .
Also the Kumano Kodo area looks impressive and I woud love to see the Nachi Taisha Fall and maybe do a little bit of hiking (no trekking)

How many days would be advisable to do this? And is it easy to do by public transport or would hiring a car be a good option here?

Thanks so much

maybe this thread will help you:
https://www.japan-guide.com/forum/quereadisplay.html?0+160337

I created an account for myself so now I am Iris1982 :)

Thanks! that is indeed a very helpful topic! Covers a lot of my questions about the onsen area
Still I am wondering if it doable though to rent a car and what the best point should be to pick it up there.

I would like to travel from Osaka by train to Koya San, but then after that maybe a rental car might make the whole trip in that area easier? Or is that not advisable? I can't find too much info on people who have done that before.

Is the area worth the trip anyway? Or would you say that for a first time visitor the Onsen near Tokyo (Hakone) is also a great experience . I have the feeling that these are much more touristy or am I wrong?
There is so much to see, I wish I could travel for 2 months haha

Or this thread: https://www.japan-guide.com/forum/quereadisplay.html?0+160413 which is more geared to having a hire car (but you could go by train from Osaka to Wakayama/Shirahama/Kii Katsura and then hire a car from there to leave the peninsula going via Koya, perhaps?)