Where It All Goes Down
Mycenae, Ancient (mythological) Greece
Sophocles wrote Electra around 410 B.C., but the play is set in an older Greece. Sophocles's audience would have identified the world of Electra as that of mythological figures. If you want to get specific, we're about roughly two decades after the end of the Trojan War.
As far as the stage set up goes, it's important to note that Apollo's statue and altar are present on stage for a good chunk of the play's action. Though Apollo never makes an appearance himself, and though the gods aren't directly involved in the action here, we're never allowed to forget their indirect involvement, at least in the minds of our characters. The divine is ever-present physically, and so is ever-present symbolically. From Agamemnon's sacrifice of Iphigenia to Orestes's stubborn dedication to Apollo, the importance of the gods is emphasized throughout Electra.