Yes, there are WiFi zones for free at Syntagma square (city centre) and Thisseion square (outside the metro station and up the pedestrian way towards the Acropolis), you'll see a lot of youngsters with laptops hanging around these places. Free WiFi zones are also available at the University of Athens buildings in the city centre and all Athens universities' campuses around the city.
At Starbucks coffee-shops there are Forthnet Wifi hotspots, you can buy a "Forthnet WiFi NetKey" card from the cashier but it's quite expensive. So you can buy a plain "Forthnet NetKey" prepaid card from any kiosk (periptero) and this will give you more time for WiFi with the same money than the "WiFi Card" at Forthnet hotspots. Go to the
www.forthnet.gr website and find out the map with available hotspots around Greece.
Also at Flocafé coffee-shops around Athens there are free WiFi hotspots and in general you might be lucky enough to find free private hotspots from offices or houses anywhere in the center of Athens. Also there are hotspots at the airport and in almost all hotels in the city, but these are not free!