As of today, Greece is still open for tourism. Here is the link to US Embassy and Consulate in Greece: https://gr.usembassy.gov/covid-19-information/
As of December 19, 2021, a negative PCR test that was taken 72 hours or a rapid test that was taken 24 hours prior to arrival must be presented to all travelers over the age of 5 regardless of vaccination status. For more detailed information, this is the link to the US Embassy and Consulate website in Greece: https://gr.usembassy.gov/covid-19-information/
You do not need to be vaccinated to enter Greece. However, you will have limited access to things to do and places to visit. Here is the link for more detailed information about vaccination status in Greece: https://gr.usembassy.gov/covid-19-information/
According to the US Embassy and Consulate's website in Greece, "All travelers entering Greece must fill out the Passenger Locator Form before travel and present the QR code received in response in order to board Greece-bound flights. Review the “Entry and Exit Requirements” section below as well as travel.gov.gr for more details." Here is the link to the Passenger Locator Form: https://travel.gov.gr/#/