I just remembered the restaurant at the Hyatt Fuji Speedway looks at Mt Fuji, didn't eat in the restaurant but did have a room with a view of Mt Fuji and it's great.
Of course adds more time to your journey, we rented a car from Mishima and drove rather then transfer to a local train to Gotemba where there is a free Hyatt shuttle.
https://www.hyatt.com/unbound-collec...talian-cuisine

Sunset Sunrise from our room.