| Cheap Flights: Austin to Budapest $469-$482 r/t [December-February] â British Airways / American Airlines / Finnair British Airways, American Airlines, and Finnair have round-trip flights from Austin (AUS) to Budapest (BUD) for $469-$482 with a connection. Flights December to February. Departures on Monday, Tuesday, Wednesday, Thursday, and Saturday. Click for more details and booking links Cheap Flights: Austin to Budapest $469-$482 r/t [December-February] â British Airways / American Airlines / Finnair . | 