Kyoto and then Koyasan or visa versa

I am landing in Osaka and then visiting the above 2 and then going to Tokyo

Would you say I go to Kyoto, spent a few days then, then go to Mount Koya for a day or 2 and then go to Tokyo

Or koya first and then Kyoto ?

Hello, I'm OSAKA citizen.

Koya first,then move to Kyoto.

Take Nankai Line from KIX to NAMBA station, (central OSAKA).

You will find rapid express train to KOYA( KOYA SAN :SAN means mountain) from NANKAI NAMBA station.
It's one hour trip to KOYA, but to visit it, a half day is not enough,I think.

After visiting KOYA, please back to Namba,then move to UMEDA by subway(MIDOHSUJI LINE,RED)where JR OSAKA station is located.

From JR OSAKA, JR takes you to JR KYOTO station within 30minutes.

or I should say Domo arigato

Apart from spending a whole day in a temple in Koyasan, staying there overnight, walking through the cementary and doing riutals

What exactly can I do in Mount Koya as I have to be in Tokyo on the 10th