I was here last week:
The Acropolis is stunning. But I also spent a good bit of time looking down from the Acropolis at this place:
This is the Theater of Dionysus. (Wikipedia gives you a better view of it.) It’s where Western drama began, where the plays of Aeschylus, Sophocles, Euripides, and Aristophanes were first performed in the fifth century BCE. And if that doesn’t make you shiver, what will?
(By the way, Mary Renault’s The Mask of Apollo gives a vivid depiction of what it was like to be an actor in the ancient Greek theater.)