SkyTeam Alliance has San Francisco to Athens on sale from $550 round trip for departures in March and April 2017. Routings via Amsterdam or Paris are options with potential overnight transit in one city or both cities.
KLM Airlines ticket with Paris overnight
San Francisco – Amsterdam AMS – Athens ATH – Paris CDG (overnight) – San Francisco
Delta Airlines ticket with no overnight transit stops.
San Francisco – Paris CDG – Athens ATH – Amsterdam AMS – Portland PDX – San Francisco