If you like hiking and doing sports you will love this mountain.
If not: I can tell you that the view is worth all the pain in your feet and legs.
During your first trip you maybe won't have much time in Japan, mostly staying in Tokyo. I'd recommend to make a day trip to Mt. Takao and enjoy Japan's nature.
On a good day you'll have the chance to spot Mt. Fuji from the top, but often you won't be lucky. This mountain is really shy and won't show itself to everyone. But anyway, it's always possible to spot Tokyo far away.
Take a second, breath and just enjoy the moment. Back to Tokyo time will fly away in a second again.