Kiso Valley (Tsumago or Magome) from Fuji

Hello I am traveling to Japan in early November and wanted to see also little bit of the country side besides the big Cities like Tokyo and Kyoto.
My plan is: Tokyo -> Fuji -> Kiso Valley (Walk from Tsumago to Magome preferably) -> Iga -> Kyoto.
So far so good, but i couldn't really manage to find good connections from around Fuji (don't know the exact place where i stay yet) to the Kiso valley and out (to Iga).
It doesn't matter if I arrive in Tsumago or Magome first, since I can do the hike in both directions.
Since I am only a student and have limited money I would prefer buses or cheap means of transportation.
Can anyone who has maybe even been there recommend me how I can access the valley good from Fuji?
And also if you think if it is worth to do Fuji -> Kiso Valley -> Iga when I only have 4/Days available. Or just general recommendations.

Thank you very much for any help i would really appreciate it!

Best Regards,
Vincent

Do you mean Fujisan? Mt Fuji?

Hi, I mean Mount Fuji or rather the area/cities around it. Like I said I have no hotel booked in a specific place there yet.