The water in Greece is drinkable but has a high mineral content which some people find upsets their tummy. If you don't wish to purchase bottled water maybe boil the tap water and keep in the fridge.
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Where in Greece has the clearest water? If clear water is what you're after, head to Balos Beach in Crete, which has some of the clearest water in Greece. What's better, Corfu or Crete? Both Corfu and Crete have incredible Greek beaches.
There are times when it cannot even be used for making tea or coffee or for cooking as the water is sometimes a brownish colour. Bottled water is used for drinking in these places. In Athens the water is drinkable but may just taste different to what you are used to.
CDC: Food and water standards in Greece are similar to those in the United States. Most travelers do not need to take special food or water precautions beyond what they normally do at home. It goes on to say to be cautious of unregulated water sources such as private wells, which doesn't concern tap water.