Mount Fuji. What's the big deal about a mountain? Well, it's a huge volcano almost 3,800 metres high (almost 12,400 ft) and is visible from places like Chiba at least 60 km away. You can see it from Tokyo Tower and the Sky Tree on a clear day (I have had the most luck in winter). It features prominently in Japanese literature, history and art. It is seen as a symbol of Japan.
You can get excellent views of Fuji from Hakone (but at the moment the spot where this photo was taken from may be closed - please check!).
From Enoshima there's a great view with the bay in the foreground.
Fujisan from the Enoshima Bridge by
RobGeraghty, on Flickr
Mount Fuji from Owakudani by
RobGeraghty, on Flickr
You can see the mountain from Mount Takao in western Tokyo prefecture.
Mount Fuji from Mount Takao by
RobGeraghty, on Flickr
If you're really lucky, you might get to see as I did the sun rise from behind Fuji at dawn on New Year's day.
The light of Fuji by
RobGeraghty, on Flickr
There's also great photos to be had around the "Fuji five lakes" with early morning reflections, but sadly I've never had the chance to do this. The photo is not by me but a Japanese photographer who is on Flickr and has an amazing collection of photos of Fujisan.