looking for a Saturday evening mass in Athens
A Catholic mass? You can locate Catholic churches in Athens on Google Maps. Clicking on the Cathedral Bascilica of Dionysius the Areopagite, for instance, turns up reviews that mention mass in English at 6:30 p.m. on Sundays (not Saturday). They don't all necessarily have web sites and directory sites also have minimal info. You could ask at a tourist office, ask your hotel to call, or try to walk by the church earlier.
Not sure what denomination you are, but why not visit a Greek orthodox service while you are there? It's a special experience, I can assure you.