Saronic Gulf islands
Hydra, Aegina and Poros are all reachable by ferry within roughly 1-2 hours from Athens' port at Piraeus, making a genuine island day trip realistic. Hydra in particular is known for having no cars — everything moves by foot, donkey or boat.
Delphi
A roughly 2-2.5 hour drive from Athens, Delphi was considered the center of the ancient world and home to its famous oracle. It combines ancient ruins with a dramatic mountainside setting — a strong choice if you want history beyond just Athens itself.
Cape Sounion
A shorter trip (around 1-1.5 hours from Athens) to the Temple of Poseidon, perched on a cliff over the Aegean — a popular half-day or sunset trip rather than a full-day commitment.
If you have an extra day or two beyond central Athens, a Saronic Gulf island trip gives the clearest change of pace — sea, quiet streets and no cars, all within a day of returning to your hotel.