Air France, Delta, and Virgin Atlantic have round-trip flights from Dallas (DFW) to Athens (ATH) for $487-$537 with a connection. Flights March, April, and December. Departures on Monday, Tuesday, Wednesday, and Sunday. 7-day minimum stay required. No Christmas dates available.
A Carry-on bag and also a personal item is allowed for free on Delta. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.