Hands down, the best place to get a covid test is the Athens airport. I suggest you take test when you land and before you arrive, as its likely that you're staying in the city and not near the airport (the airport is a bit of a drive from downtown Athens). There are antigen and PCR tests that allow for a day long window, meaning you don't need to arrive at a specific time to take the test. There is usually a bit of a wait but the process is smooth.
Here is the link: https://athensmedicalgroup.com
Here is the link: https://athensmedicalgroup.com