Below are two pictures of various money changing/money wiring establishments of which Omonia square as at least 5 and they keep longer hours than banks and have shorter lines and better rates too usually.
Below we have the Post Office with extended hours which resides at 100 Aeolou Street across from Starbucks. Far left are the 24 hour a day bins you can use to post your already properly stamped mail. Click to see what box goes where. Center is the interior of the PO and pay special attention to the ticket dispenser on the right which will issue you a numbered ticket. After obtaining it sit down and wait for your number to be chimed on the digital displays above head level. Then follow the arrows to the correct numbered window. Finally far right is a stamp dispensing machine which is accessed through the door to the left of the main post office door and is sometimes open even longer hours than the extended ones of the post office.
Read more about Greek Post Offices.
Here below left and center are two pictures of the International Book store in Omonia Square which in my view is a very handy addition to the square if you like to read. And below right is something you may find handy: automated left luggage lockers with a 15 day max period. You will find these in the metro station below.