Greek tourism minister Harry Theoharis has announced that the country is opening its borders on May 14. He said that all persons who have been vaccinated or who test negative could travel to Greece this summer.
“Tourists will be welcome if before travel they are either vaccinated, or have antibodies, or test negative. All tourists will be subject to random testing,” the Minister explained. -- Greece to Welcome EU & non-EU Vaccinated Tourists From May 14
So the next question to ask is "what's the covid situation" i.e. "are they just desperate for healthy tourists?"
Here's where things get a bit muddled. While states like California have seen a dramatic decline in infections and death, Greece hasn't seemed to fare so well.
So you have a decision to make, based on your own risk assessment.
Meanwhile, here's a map of Greece and Greek Island Groups. And when you go to Greece, you probably want to plan a trip when the weather is to your liking, so here's access to Greek weather charts for select cities and islands.