We went island hopping (I think there's a really good book of the same name) in '06. Alonissos and Skopelos were very nice. Especially the former. To a certain degree I didn't mind Skiathos as we were away from the package resorts.
We went by bus from Athens to a ferry port in the north and took a SeaCat out to Alonissos. We then flew back to Athens from Skiathos. It was a nice little adventure.
We went to Agni, Corfu in '10. A very small little beach hamlet down a steep singletrack road on the east coast of the island facing Albania. Amazing. There are very few places to stay. I think two. An apartment which we had that's part of the house owned by the family that run one of the tavernas and a cottage to let.
There's a wonderful little beach and a larger beach/cove a 10 minute coastal walk away. We hired a boat and travelled up and down the east coast finding our own little secluded spots to drop anchor and spend the day. Truly amazing. The tavernas at Agni were top notch and lots of 'big' boats and their owners and entourage would come for lunch so nice for people watching/watching the world go by too.
I've always said I'd never go back to the same place twice as the worlds a big place but I'd like to go back to Agni.
EDIT: I might add that without hiring the boat you're very, very secluded/isolated so it's a must.