Greek Post Offices open at 8 am and close at 1:30 pm Monday thru Friday. Sometimes you may find one open until 2 or even 3 pm. They are closed Saturdays and Sundays. Take a number from the dispenser immediately upon entry!
In addition to Post Offices, Greek Stamps may be purchased at some periptero's and kiosks depending on the area you are within Greece. There are stamp machines in larger post offices usually in an alcove somewhere.
Smaller Greek villages and hamlets may not have an official Post Office and its function may be preformed by a local merchant with more flexible hours and rules.
It is highly recommended to buy Greek stamps for your primary mailing destination all at once. Stamps for a post card within Europe will cost less than stamps for a Post card to the USA. The same for letters. Enquire from the tellers and buy stamps all at once in advance. It will save you time in line. The Greek Post Office in Athens' Constitution Sq.->
There are different mailboxes outside for differing destinations within Greece and the World. Read carefully!
If you have anything really important to mail send it registered or 'Sys-tee-men-no'. Cost about 2.70 EU (Checks, credit card payments etc!)