American Airlines, British Airways, and Iberia have round-trip flights from Dallas (DFW) to Athens (ATH) for $519 with a connection. Flights April to May. Departures on Tuesday and Wednesday. 14-day minimum stay required. We’re not seeing this price for shorter trips.
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.