Many travelers who plan to visit Turkey also add Greece to their wish list. It is very easy to travel between the two countries and they share quite a lot of history. You can find traces of Turkish occupation in Greece but there are also ancient Greek sites in Turkey.
Getting from Istanbul to Athens is quite easy. If your vacation days are limited, do consider flying between the two cities. It is not that expensive and the prices depend on the time of year when you plan to travel. Direct flights in late August start at €126 per person one way (with Olympic Air), while if you plan to fly in early September, you’ll save a bit (€100 per person, one way with the same airline).
There are also ferries connecting Turkey to Greece. You can from Turkey to Rhodes, Chios, Kos and Lesvos by ferry. This is a lovely choice if you aren’t rushed by a tight schedule and if you really like to soak the atmosphere. Of course, you can always choose the ferries in Greece to explore more islands.
Do remember though that both the ferries between the two countries and the ferries within Greece depend on the weather and season. By the end of September the number of daily connections are limited and sometimes the ferries stop working over the late fall and winter.