American Airlines, Finnair, and Iberia have round-trip flights from Austin (AUS) to Mykonos (JMK) for $869 with one connection each-way. Flights in October. Departures on Sunday. 8-day minimum stay required. An overnight stay in London is required on the return leg of the trip.
Getting to this island of Greece usually requires about $1300 and multiple stops due to the smaller airport and location. Pay attention to your flight times and monitor them for changes after you book. Smaller airports have more volatile scheduling, so schedule changes are more likely to happen when compared to larger airports.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.