This is very cool. I'm told you can see Mt Fuji from Tokyo on a clear day, but I never managed to see it. I did manage to see Mont Blanc from my Kitchen in Lausanne, Switzerland a few times - such a beautiful sight.
Mt Fuji is only about 100km away from Tokyo. Main problem is there are tons of buildings blocking your view, but if you're at a high enough floor you can see the it even when it's a bit cloudy. For example, see the last pic here: