I was wondering where are the post offfices in Japan, specifically around Shinjuku, and what time they open daily. I'm planning to mail back some things I'm buying there due to airline baggage restrictions. Thanks!
The post office Dutch Baka san mentioned is one of the special offices (Delivery post offices), they are handling posts (including parcels) 24 hours a day. From 0:00 to 9:00am, and 21:00 to 24:00 there is a small door to let in people (I don't know about this particular post office but normally they have a door on its side apart from the main entrance in the front) during those hours. This service is also available on Sundays and public holidays.
For this special 'side door', you should look for the sign sayingﾂ 窶堙､窶堋､窶堙､窶堋､窶倪?ｹﾅ津ｻ (yuu yuu madoguchi).