Corfu is definitely my favorite Greek island. Been there most of my summers. In my opinion Corfu has it all, it doesn't matter the reason you're there for. The island has something for everyone :-)
I also really like the island of Corfu. We stayed in the Kalamki-area, which was very nice, and the beaches was small and secluded, and actually not crowded at all.
The nicest island i have been into of this few i have been on is Creete (Kalymnos, Kos, Santorini).
Cos Creete is big and you could rent a cab and visit your own golden spots as you like i have found mine there as Paleochora, Elos taverna, Falassarna and Elafonisi.
Korfu - Kerkyra! Don´t ask me why, I just love that island.
The beach outside Dassia and the whole area north & west of Dassia.
You should go there in the beginning of the touristseason!
I like Santorini too but I'd also like to mention Paros, lovely island where we rented vespas and went to small villages where they didn't even speak any english..Very exotic for being in Greece!
I think my favorite is Santorini.
It's a small and romantic island with black sand on the beaches.
When we were there we rent a lovely little room with two floors and a
princessbed =)
I love the white houses with blue details, so typical for Greece. Haven't been there for quite some time, maybe it's time for another holiday there? Have you got a favourite place in Greece?