This is the Tokyo Metropolitan Government building, which we call Tocho (都庁) in Japanese.
Formerly located near Tokyo Station, Tocho was moved to Shinjuku in 1991 because the former building was too old. At that time, it was the tallest building in Tokyo.
They have an observatory on the top floor, which is a popular tourist spot, and you'll see a fantastic view of Tokyo. Plus it's free. Unfortunately, I took these photos about a week after the March 11 earthquake and the observatory was closed. But I hear it opened again this month, so if any of you visit Shinjuku, this is a great place to go!
Enjoy looking at more beautiful skies all around the world here.