The Shinjuku Government Building is the tallest building in Shinjuku and gives you a fantastic view of Tokyo, especially at night! Visit in the evening for a stunning night view and with clear weather during daytime you can see Mount Fuji. You’re allowed to take photos, however the use of a tripod isn’t.
Take the West Exit from Shinjuku JR Station and follow the signs. Walking takes about 10 minutes.
The North Observatory is open from 09:30 to 23:00 and is closed on every 2nd and 4th Monday of each month.
The South Observatory is open from 09:30 to 17:30 and is closed on every 1st and 3rd Tuesday of each month.
Closing days may change depending on National Holidays. Both of the Observatories will be closed on December 29 – 31 and January 2 – 3.
Of course things may change so always check the Shinjuku Government Website (in English) for the latest details: http://www.metro.tokyo.jp/ENGLISH/OFFICES/observat.htm