Greece Has Reopened to TravelersâHereâs Everything You Need to Know Courtesy of onefinestay Conveniently, luxury home rental service onefinestay just launched a collection of villas in Mykonos and Santorini. On April 19, after 14 months of border closures, the Mediterranean country began to reopen to international travelersâincluding Americans. Is it time to make our Greek getaway dreams come true? share this article On April 19, the Greek government announced that a phased reopening had begun, marking the first time international travelers could visit since the borders closed in March 2020. Thereâs been a rush of interest in trips to Greece since, according to AFARâs trusted travel advisors, but a question lingers: