For a couple months in Winter, Mt. Fuji is often visible from many locations in Tokyo at a suitable altitude, including Skytree, the Tokyo Metropolitan Government Building, and Roppongi Hills. While Mt. Fuji is probably the icon of Japan, it is surprisingly shy about appearing. Winter is the most likely season to see Mt. Fuji from Tokyo whereas in Summer, perhaps only on the day after a typhoon when the winds clear the skies. Many people think the best view of Mt. Fuji is from the top, but from people I know who have climbed it, it is much more photogenic when viewed  from afar.