Mt. Ryugatake in Yamanashi (not to be confused with other mountains with the same name in other prefectures) is one of the best places to enjoy the view of Mt. Fuji together with the vast forest underneath.
It’s an easy 90 min hike from Lake Motosu to the view point. If you want to enjoy more than just the view, there is another trail which takes about 5.5 hours return.

It takes about 2 hours from central Tokyo to Mt. Ryugatake by car, or 3.5 hours by train + bus.