We would like to fly in and out of Istanbul. We would like to visit one Greek island...one which would be easy to take a quick flight or possibly a ferry. We have already been to Mykonos and Santorini. We have also already been to Istanbul. We plan on spending about four days in Istanbul and a week in a Greek island. We don't like to jump all over the place. That is why we try only to visit two main places each time we vacation in Europe. Thank you for your advice.
I would suggest you try the island of Rhodes. It has everything--fortress, ruins, beaches, beautiful scenery, good food and wine.
There are no ferries from Istanbul to any Greek island. To reach a Greek island from Turkey by ferry will take you at least one full day, perhaps two, depending on which island you choose, since you will first need to make your way to a Turkish port that offers the ferry. Lesvos is closest Greek island to Istanbul so that would be the best choice timewise if you choose to go by ferry. To reach Lesvos by ferry you will depart from Ayvalik, Turkey. If you are planning your trip for sometime during the summer months between June and the end of August you can fly from Istanbul to Mykonos, the only island which can be reached directly by air. It's either Pegasus Air or Atlas Jet that flies there, I can't remember which. From Mykonos you can catch a ferry on the same day to one of several islands, then reverse your route to return to Istanbul.
You may want to consider visiting the Princes Islands which are not far from Istanbul via ferry - at least one or two have Greek origins and at least a small population. They are very laid back and lovely. http://www.wittistanbul.com/magazine/why-and-how-should-you-visit-the-princes-islands-in-istanbul/
Kos and Rhodes are good islands for what you're looking for.