Delta, American, British Airways, United and various other airlines have round-trip flights from Houston (IAH) to Athens (ATH) for $502-$532 with a connection. Flights March, April, November, and December. Departures on Monday, Tuesday, Wednesday, and Sunday. Holiday blackouts.
Cheapest fares in March and April.
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.