American Airlines has round-trip flights from Houston (IAH) to Athens (ATH) for $465-$505 with a connection. Flights in October. Departures on Wednesday and Sunday. 7-day minimum stay required.
Greece plans to be fully open to vaccinated tourists by May 14th.
They still allow free changes for Main Cabin and higher classes. Carry-on bag is allowed for free. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.