Piraeus is the obvious launchpad for the Saronic Gulf islands. Aegina, the closest, is forty minutes by hydrofoil and works as a half-day or full-day trip. Hydra, two hours out, is the prettiest and pedestrian-only — no cars, just donkeys and stone alleys.
In the other direction, central Athens is twenty minutes away on metro Line 1; the Acropolis and the Plaka district can be done as an easy half-day from Piraeus.