Three islands carry most first trips, and each one is built for a different kind of week. Santorini is the view, Mykonos is the social one, and Crete is the place to go when two islands already sound like a lot of packing.
Santorini: Caldera and Akrotiri
Santorini is the rim of a volcano that erupted about 4,500 years ago, and Fira and Oia sit on the cliff edge above the flooded caldera. Red Beach and the Assyrtiko vineyards fill the hours away from the view. The Akrotiri excavation is the stop people skip: a Minoan city buried under volcanic rock and dug out largely intact. Without a car, the villages and the excavation are easier on a Santorini tour than on the local buses.

Mykonos: Town, Windmills and Delos
Mykonos earns its reputation twice. The alleyways, blue-domed churches and windmills belong to the afternoon, and the beaches and nightlife to the hours after dark. The boat to Delos is the reason to stay a second day. The crossing takes about 30 minutes, and the island is an archaeological site rather than a resort, with a Hellenistic city built in the fourth century BC, mosaics, the Theatre of Delos and the Temples of Apollo. A guided Delos trip runs about four hours, which fits a morning.
Crete and Naxos for a Slower Week
Crete is the largest island and the one with the most range: the palace of Knossos, the Samaria Gorge walk, beaches such as Elafonissi, and a food culture built on olive oil, cheese and mountain herbs. Naxos is the family answer to Mykonos, with wide sandy beaches, the Portara gate and mountain villages, and it costs less than the two famous islands.
Rhodes, Corfu and the Second Week
Rhodes brings medieval history to a beach trip: the Old Town is UNESCO-listed, Lindos has its own acropolis, and Tsambika is the sand day. Corfu, in the Ionian Sea, looks nothing like the Cyclades, with Venetian architecture, green hills, and hiking trails. Both suit a second visit better than a first one, because each pulls you off the Athens-to-Santorini line.