| Cheap Flights: Austin or San Antonio to Athens $534-$559 r/t [March-April] â American Airlines / British Airways / Finnair American Airlines, British Airways, and Finnair have round-trip flights from Austin or San Antonio (AUS, SAT) to Athens (ATH) for $534-$559 with a connection. Flights March to April. Extended weekends available. Click for more details and booking links Cheap Flights: Austin or San Antonio to Athens $534-$559 r/t [March-April] â American Airlines / British Airways / Finnair . | 