It makes a while I am testing the best view points around Tokyo. It's not always easy as the weather needs to be fair, particularly in order to see Mount Fuji, which occurs most often in the winter.

My favourites are the following :

1) Revolving restaurant at the 17th floor of the New Otani Hotel, Akasaka. Not only does is offer a perfect 360degrees view, but its central location allows to see the whole of Tokyo at equal distance, from Shinjuku to Otemachi or Shimbashi. The only drawback is that you have to pay and just a tea/cofee will cost you at least 700yen.

2) Shinjuku's Tochou “s’¡ (Tokyo Metropolitan Government Towers). It's free and at the top of the 45th floor it's probably the highest place you can go in Tokyo. The view on the surrounding skyscrapers is fabulous, especially at night. Mount Fuji is well visible during daytime - beware, however, that even if the sky is blue, it might be hazy in which case, you won't see anything. The main weak point is that the other main areas of Tokyo (Imperial Palace, Otemachi, Akasaka...) are too far away to be appreciated.

3) The Yurikamome (monorail) ride from Shimbashi to Odaiba pass above most building and gives a great view on the bay of Tokyo, Rainbow Bridge (that you actually cross), Shimbashi new scyscrapers and other towers such as the Triton center in Kachidoki or the blue and orange Tsukuda appartment towers.

4) Ebisu Garden Place Tower. You can go for free at the 2 top floors (about 35 floors), which have plenty of restaurants in the midst of a splendid Graeco-Roman mythological decoration. You can see Shinjuku, Shibuya, Akasaka, Mount Fuji and even Yokohama.