Athens airport is new and pretty nice, but we didn't find a mobile carrier store. Instead we asked our driver to stop at one on the way into town. We chose Vodafone. He did, and we bought 3 SIMs. The process is pretty easy, and 500mb costs only €10 each. (1 gig is €20 if you feel like a data hog.) They copied my passport and registered all three me.
It worked well even on Santorini, one of the Greek islands. The SIM was locked so make sure you carry the lock code with you. Occasionally I would lose network connectivity - it would appear to be connected but no data would flow. I switched to airplane mode and back to reconnect. Also, I saw noticeable latency. For the price, great service.