Athens, Mykonos and Santorini give this ten-day trip three different settings: marble temples above a modern capital, whitewashed harbour lanes with a beach nearby, and villages perched above a volcanic sea basin. Two nights in Athens allow one main sightseeing day before three nights on Mykonos and four on Santorini. The Acropolis and Delos explain different sides of ancient Greece; the final island adds the caldera, a boat excursion and a winery.
This is a trip with two substantial travel days, rather than ten uninterrupted sightseeing days. Fly into Athens, follow the ferry route south and look for a flight home from Santorini, either direct or on a suitable connection. Stay in Fira for all four Santorini nights and take the bus to Oia. Keeping three overnight bases gives the last part of the trip more time than a Fira–Oia hotel move would. May, June and September generally suit this plan better than peak summer, when accommodation and popular departures are under greater pressure.