Where It All Goes Down
A barren cliff in Scythia; a rock
Here's the thing about Prometheus Bound: you could act it anywhere. You could perform it at the Globe; you could perform it on a high school stage; you could perform it in front of your house. All you'd need is a rock. If you were a good actor, you wouldn't even need a rock—you could just, well, act like you were chained to one.
That's because setting just doesn't matter in quite the way we might expect. It's honestly not that important where the play takes place—although we know that it's a barren, desolate region.
Ancient Scythia covered a large area stretching from the Black Sea into central Asia. In the eyes of the Ancient Greeks, the inhabitants of Scythia were among the most barbaric on earth. According to "historian" Herodotus, the Scythians didn't have cities, forts, houses, or agriculture. So, basically nomads.
Now, we certainly don't think nomads are barbarians or anything, but the point is that this is basically city folk—the Athenians—looking down on the country folk. It's like taking a born-and-bred New Yorker and exiling him to North Dakota.
Another thing about North Dakota—er, Scythia—is that it's sparsely populated. We're not sure about this, but it seems like being chained up in a barren location is a perversely fitting punishment for Prometheus's "crime" of helping humans. Want to help people? Great. We'll make sure you never see another human being in your entire, immortal existence.