The Tokyo Metropolitan Government building houses the local government headquarters of the whole Tokyo Metropolis. It is located in the Shinjuku Ward of Tokyo. On the 45th floor, two different towers of the building have observation decks and they are open to the public and free. The decks also include souvenir shops and cafes.
I've been to the building four times and definitely want to go back. Each time I went up, I saw different views, depending on the weather and time of day. One day it was so clear, I got a great view of Mt.Fuji.