With hundreds of miles of coastline around Athens and Attica it is no surprise that there are lots of places to Scuba dive, never mind the many dive clubs and scuba stores around.
Most of the best diving around Athens is to the south around Voulgameni and towards Sounio, where the rocky coves become deep suddenly. The east of Attica is also popular for diving and has some clubs. Athens is often an entrance point to Greece by many divers heading towards the more recognised dive centres in Santorini, Paros and Crete, and miss out on some great dives around Attica.
The laws in Greece were once very strict when it came to diving in their waters, so many areas of Greeces' coastline were prohibited due to the many archaeological sites and shipwrecks found and still to be found. I believe at one point only about 20 percent of entire coastline could be dived. Thankfully in recent years the laws have changed making Greece much more Diver friendly, trying to attract more Diving Tourism.
The Mediterranean has be labelled as a dead or dying sea with not much marine life to look at, many divers prefering the red sea or Thailand. But from my own experience the Mediterranean around Greece has lots of marine life, I've seen everything from Tuna over a metre long to Barracuda the size of my leg. I regularly see Octopus, squid and Cuttlefish as well as the many other types of fish.
As with many other countries, to go on organised dive trips or rent equipment you will need a recognised qualification and license wherever it be BSAC, PADI or one of the many more Dive organisations. Greece does have many laws about diving in their waters so it is best to check up on these laws before coming.
If you need more information or would like to try diving in Athens I can recomend Aqua Divers Club, it is only about 48km to the south of Athens in Anavissos and has 25 different dives.
Snorkelling can be done by just about anyone, all you need are a mask, a snorkel and fins. As with diving the rocky coastline of around Athens is perfect for snorkelling as there are lots of marine life close into the shore. Once again the best places for snorkelling is the coastline down towards sounio and after Voulgameni.
Kineta (about 40 mins from Athens towards Corinth) has some excellent spots for snorkelling with a lot of marine life. If you are a big fan of shell fish like mussels and Oysters, then Neraki (20 mins from Athens) is a perfect for you. With a mask and snorkel you can easily collect the shell fish not far from the shore.