If you are visiting several cities on the way to Tokyo from Osaka, I would suggest that you take local train and highway buses, depending on where to go.
If you are going from Osaka to Kyoto, you can take either Shinkansen or local rapid train. If you do not have a JR
pass, local train would be better because it is a lot cheaper and it does not make much differences in terms of travel time.
From Osaka to Hida Takayama, a train(Limited Express Hida) might be the easiest way to get there as there are no Shinkansen between Osaka and Takayama. From Takayama to Shirakawago, please take a bus from Takayama
Nohi Bus Center. You might want to book or purchase a ticket beforehand as the route is very popular for tourists.
If you are going to Mt. Fuji, please go back to Takayama from Shirakawago and then, take a highway bus. The highway bus will take you to Kawaguchio. If you want to go to Mt. Fuji 5th station, you can take another bus from Kawaguchiko to Mt. Fuji 5th station.
From Kawaguchiko, you can take a highway bus to Tokyo.
You might want to book your ticket in advance from the following website
I hope this is clear to you.
Have a nice trip in Japan!
Japan Trip Search