Mt. Fuji is basically synonymous with Shizuoka Prefecture and vice versa, although it also belongs to Yamanashi Prefecture. Since the “front” side of Fuji is in Shizuoka (as seen from the shinkansen), the mountain is more associated with Shizuoka (unless you live in Yamanashi).
The upper photo was taken from the highway (Tomei Expressway) on a late winter afternoon. I like this shot because it has no apparent man-made objects. No buildings, train lines, cars, nor unsightly smokestacks. Only a green forest and pampas grass. A rare shot. Just seconds after I took this shot, rural factories, etc., came into view. (Right above the tree line in the far distance, there are actually power line towers across the foot of the mountain, but hardly noticeable.)
Lower photo was taken shortly before sunset in Fujinomiya. Under the right conditions, there is indeed such a thing as a “Red Fuji” as depicted by Hokusai’s famous woodblock print. This photo was taken in January.
As with cherry blossoms, we can never get tired of seeing Mt. Fuji. Just so majestic. Fills you with awe each time, even from a far distance. Been that way for centuries. Such timeless elegance. An inspiration to artists and poets for centuries.
Climbing Japan’s highest mountain is also an unforgettable experience. Highly recommended while you’re still young and able. I won’t do it again though. In summer 2020, Mt. Fuji was closed to climbers due to Covid-19. One problem is the mountain huts. They are cramped spaces, especially the bunk beds with no partitioning. You sleep like sardines on a long, padded deck. Bedding is musty too. No open windows and cross ventilation due to cold winds. That’s how it was when I was there. Lucky I didn’t get asthma. In summer 2021, Fuji reopened to climbers and the mountain huts limited the number of lodgers.
If it’s possible, a recommended alternative is to take the bus halfway up the mountain to the 5th station (Fuji-san go-gome 富士山五合目) without climbing the mountain. The mountain road is called “Fuji Subaru Line.” No problem as a day trip from Tokyo (2.5 hours from Shinjuku) or the Fuji Five Lakes area in Yamanashi. The views from the 5th station are nice enough on sunny days. It’s also the starting point for most climbers. Browse the gift shops and lookout points, then take the bus back. 
Bus: http://bus-en.fujikyu.co.jp/highway/
Mt. Fuji: http://www.fujisan-climb.jp/en/