| Cheap Flights: San Antonio or Austin to/from Belize City $284-$294 r/t [October-August] â American Airlines American Airlines has round-trip flights from San Antonio or Austin (SAT/AUS) to Belize City (BZE) for $284-$294 with a connection. Flights October to August. Weekends available. Origin/Destination reversible. Click for more details and booking links Cheap Flights: San Antonio or Austin to/from Belize City $284-$294 r/t [October-August] â American Airlines . | 