December to February
Best months. Dry air, low humidity, snow cap visible. Mornings are sharpest, especially the hour after sunrise.

From the city
Short answer yes, on a clear day. Long answer depends on the season, the time of day, the building and a little luck with the haze.
Fuji is visible from Tokyo on roughly 80 days per year. Almost all of them are in winter.
Best months. Dry air, low humidity, snow cap visible. Mornings are sharpest, especially the hour after sunrise.
Decent in early morning, hazy by lunch. Sakura season adds the Tokyo-foreground shot.
Worst. Rainy season, then humid summer haze. Fuji hides for weeks at a time.
450 m up. On a clear winter morning Fuji floats above the Kanto plain to the southwest. The single best paid view in the city.
Lower than Skytree but closer to the southwest skyline. Fuji frames neatly between Roppongi towers.
Open-air rooftop, 230 m. Sunset is the photographer's hour. Fuji silhouettes the western edge.
Free. North side of the building, west window. Locals' tip for a no-cost Fuji shot.
West-facing windows look straight at Fuji about 100 km away.
Marukobashi and Futakotamagawa. Open horizon to the southwest, no skyscraper blocking.