My favorite island in Greece is Santorini. If you can only make visit one island make it Santorini. Loaded with great boat tours, wine tours, fantastic hotels, amazing restaurants, and awesome things to do. Along with Crete, Santorini is the best island in Greece in the winter and shoulder seasons when it still has plenty to do.
The best nightlife and clubbing in Greece is found on Mykonos. Also has great beaches and a surprisingly charming capital village, Mykonos Town.
The largest Greek island and rich with beaches, historical sights, hikes, and small cities. So big that if you only have a week it’s good to limit yourself to only this island. If you have two weeks it makes a great pair with Santorini.
The most family-friendly island in Greece is Naxos. Great beaches and the main town is crammed with wonderful tavernas serving some of the best food on the Greek islands. The inland villages are marvelous to explore.
If you want quiet idyllic beaches, an unhurried charm, and fantastic local restaurants then Antiparos is a great choice. It’s reachable only by boat from nearby Paros.