There are lots of options. The problem is that Mount Fuji is often not visible due to clouds or low visibility.Your chances are best early in the morning (before 9am) and by being as close to the mountain as possible. Winter months tend to have better visibility than summer months.
Having said that, it is probably easiest to visit the Fuji Five Lake area:
http://www.japan-guide.com/e/e6905.html
An alternative would be Fuji City in the south of the mountain, where the famous photos combining shinkansen trains with the mountain are made from. You can get there by shinkansen:
http://www.japan-guide.com/g4/2019_01.jpg
On clear days, you do not even need to leave Tokyo, but can see the mountain from the city, especially from observation decks.