better itenary

Hello Jocelyn!
I believe it is best to do Tokyo > Hakone > fuji > Osaka. 
From Hakone youll have a great view from Mt Fuji before you actually go there. Also, Hakone is on the way to Mt Fuji so the itinerary makes more sense.

Have you taken a look at the itinerary pages here in Planetyze?

Tokyo itineraries:
https://planetyze.com/en/japan/tokyo/itineraries

Hakone Itineraries:
https://planetyze.com/en/japan/hakone/itineraries

Mt Fuji Itineraries:
https://planetyze.com/en/japan/mount-fuji/itineraries

Osaka itineraries:
https://planetyze.com/en/japan/osaka/itineraries

I hope this helps!
Have fun!