GR - which island?
I've only been to Naxos, Santorini, and Crete. But we will be back again this spring and I need to decide on an island for a 1 week stay. I generally like to stay in one place for a week more than jumping around. Naxos was a good food island more rustic and genuine. The south side of Crete and the mountains were nice too, but Santorini and Crete on the north side were too expensive and skewed to the English and German tourists.
Extended family in Athens have a house on Chios, and thought about going ther with a side trip to Turkey if time allows...
Absolutely loved Sifnos. Very small island with a distinct culinary tradition. Wonderful low key place to stay - we had a room almost directly on the beach in a tiny village with a dozen tavernas. Not good if you want excitement, but excellent for independent exploration.
Have been to many islands. Chios is not my favorite. We planned to take a boat acrocc to Turkey but the boats were not running and we had to get a boat ride from a friend of a friend who knew the Mayor. Big pain.
Our most favorite island is Hydra. Very small, very quiet (no cars or motorcycles) but beautiful. Lots of good eats. You must walk everywhere or take a donkey. The nicest hotel which has a pool is Bratseras- in an old sponge processing factory. Very near to the port.There is also a charming guest house called Miranda. There is not much to do and the main harbor where you land has no beach- you go to the rocks for sunbathing and dive off into the sea but if you stay at the Hotel with a pool it is even better. Many very good restaurants. You can take a water taxi to the other side of the island to the beach.
Another wonderful island with many more things to do is Cephalonia. The best part is you can take a day trip to the beautiful little island of Ithaki (Ithaca). Not extremely touristy.
We also love Corfu (Kerkira). Now, Corfu is quite large and you will have a lot to do there. So if you are looking for lots of sightseeing, nice drives, many beaches etc. this is the place. Hyrdra is for a lazy time in a beautiful place and Cephalonia is in between.
Another suggestion is to drive from Athens to Mt. Pelion. Such an amazingly beautiful place. The villages of Macranitsa and Tsagarada are wonderful. Tsagarada(not sure of spelling) has a fabulous beach. Wonderful restaurants. It is about a 3 hour drive from Athens.
If you are looking for a non-touristy island, which it sounds like you are, Chios would be a nice place to go. Another island nearby Chios that you might like is Lesvos. Both these islands will give you more of a genuine island experience than do places like Corfu that have a thriving tourist industry. Of course, if an island isn't a tourist mecca, it may not have the same easy infrastructure for tourists that more visited islands do. But if you're independent, and don't mind renting a car, you can have a very good time on places like Chios and Lesbos. Also, if you are going places where you have family, you'll probably get a warmer welcome and a more genuine experience than if you go someplace where you are a complete stranger.
re: Laurie Constantino
Also, your foodie dollar goes farther on an island like Lesvos(aka Mytilini). Last September, I was eating like a queen on Lesbos for 2/3 (sometimes 1/2) the price of what I had been paying in Mykonos, Santorini and the larger cities in Crete, and the quality was usually better.
The fish restaurants in Sigri, a small fishing village on the west coast of the island, are known throughout the island to be particularly good (especially the Cavo di Oro -Golden Key).
I also had amazing meals in Mytilini town (the capital), Molyvos (O Faro in the harbour), Vigla (To Balkonaki) and Gera.
I would recommend Rhodes. I have been to Chios last - I would say that the others here have commented well about what you can expect in Chios.
However, no-one has mentioned Rhodes, which I think would take about 1 week to visit. There is 1 wonderful restaurant recommendation that I can make - Kioupia. It is hard to get to however. They have recently opened another one in the northern area of Athens, Kifisia. However the original restaurant is in Rhodes. Fixed menu, with fixed price. No way to finish the entire meal. Excellent food. At one time it was one of the top restaurants in Greece.