Islands

Unfortunately, islands are not my preferred places, so I can't help you much :(

Ionian Sea islands are a different side of Greece, influenced by some Italian customs and architecture, particularly Kerkyra (Corfu), Kefallonia and Zakynthos. As long as these islands are very next to Italy, I suppose most of you want to visit Aegean islands, so I won't describe them at the moment (although they are also very picturesque).

Aegean Sea (Archipelagos) islands are divided in 4 geographical regions, each one having it's own physical and cultural particularities. The famous Crete is another island, the largest in Greece and very different from the rest, a large chapter that will be covered in the future.

NORTH AND NORTH-EAST ISLANDS (Thassos, Lesvos, Chios, Samos, Limnos)

In contrast with central Aegean Sea islands, these are wooded (partially) and fertiled. Tourism is not the basis of their economy. From the architectural point of view, the most exciting is Chios, an island where Greeks and Italians (Genoans) created a fine culture during the years 1300-1800. Although the island was almost completely destroyed by the Othomans during the Greek revolution in 1821 (100.000 innocent civilians killed or made slaves), the castle villages and a special sense of nobility still remain through the ages.

NORTH-WEST ISLANDS or "VOREIES SPORADES" (Skiathos, Skopelos, Alonissos)

Located near Pilion peninsula, Skiathos and Skopelos are wooded islands with nicest beaches. They attract thousands and thousands of people during summer, so accommodation is difficult. You can easily go there from the port of Volos or directly from Piraeus. On ship between Volos and Skiathos, you can admire some of the beauties of Pilion, the area of Trikeri and the nearby island. Exiting Pagasitikos gulf, you can see the spectacular view of Evia, Pilion and South Thessalia.

CENTRAL AEGEAN SEA or "CYCLADES" (Paros, Naxos, Mykonos, Santorini, Delos etc)

The most known Greek islands, maybe THE islands, at least for the foreigners. You have already seen something of them in postcards, magazines etc. Northern big islands like Naxos, Andros and Tzia are not so dry as the rest of them.
In summer, they attract an enormous number of tourists. Mykonos is the by far the most expensive and "high society" place, being also a gay paradise. Santorini is next to Mykonos, regarding to night-life. Santorini (officially named Thira, it's ancient Greek name) actually is part of a large volcano (the rest of it lies in the bottom of the sea, after the enormous eruption at 1500 B.C that destroyed the magnificent prehistoric civilisation of Cyclades and Crete). A must-see, as long as Delos island which is an enormous archaeological site. Paros has also a rich social life (e.g. Naousa village), although it is not as expensive as Mykonos or Santorini. If you go to Paros, then you must take a look at the small island of Antiparos. Other large islands are Syros, Tinos, Kythnos, Serifos, Sifnos, Amorgos, Milos, Ios (rockers and other alternative people were attracted in Ios in the past, I do not know if the same happens today).
If you plan to visit the smaller, quiet and not so "touristic" islands, you must know that they can be approached by infrequently passing ferries (we call them "agoni grammi").

NORTH-EAST ISLANDS (Rodos, Kos, Karpathos, Patmos, Kalimnos etc)

We call them "Dodekanisa" (twelve islands) because twelve are the larger of them. Rodos and Kos are not so dry, the rest of them are wooded in the same amount as the Cyclades. Rodos, the capital island, is the most known (ancient sites, medieval castle, night life etc). Patmos is the "holy island" because of the fortified monastery of Agios Ioannis (St. John the Evangelist).