Day 1 — Acropolis & Museum
Acropolis at opening time, followed by the Ancient Agora on the way down, then the Acropolis Museum in the afternoon. Finish with an evening walk through the Plaka neighborhood for dinner.
Day 2 — Central Athens
Syntagma Square and the changing of the guard, the National Garden, Panathenaic Stadium (site of the first modern Olympics), and the Monastiraki flea market area in the afternoon or evening.
Day 3 — Day Trip
A Saronic Gulf island (Hydra or Aegina) or Cape Sounion, depending on whether you want a full island day or a shorter half-day trip.
This covers Athens' core sites plus a genuine change of scenery on day three — if you have a 4th day, Delphi is the strongest addition for travelers who want more ancient history.