Tokyo Metropolitan Government Building (東京都庁) has the observatory on the 45th floor. The building has two towers on the top levels, and both of them have the observatory. It is one of the famous spot to see downtown Tokyo, especially for night scenery.
Tourist Info.
Admission: Free
Open from 9:30 to 23:00 (south tower closed at 17:30, and last entry is 22:30.
No Smoking, No food.
Access
0. at Shinjuku Station
1. walk west (15 min.)
45 min
New Wave Samurai Movie. 
映画好き集まれ！ 
The altitude of the observatory is 202m. There are gift shop and restaurant on the both towers.
The tower is 243.4m high, and built in 1990. It was the highest building when it's built and still highest building in Shinjuku.
Web site of the gift shop: http://www.hakuhinkan.co.jp/