| Cheap Flights: San Antonio to Athens $670 r/t [October] â American Airlines American Airlines has round-trip flights from San Antonio (SAT) to Athens (ATH) for $670 with a connection. Flights in October. Departures on Monday, Tuesday, Wednesday, and Sunday. 7-day minimum stay required. Greece is aiming to reopen for tourists on May 15th (Reuters). Click for more details and booking links Cheap Flights: San Antonio to Athens $670 r/t [October] â American Airlines . | 
