I'm writing from Naxos, a beautiful island in the Cyclades. I haven't seen many Greek islands, but so far Naxos is probably my favorite. It is a big island that has its own economy separate from the tourist trade, so while there are plenty of tourist-oriented shops, tours, and sights, it feels like there's more going on here than just catering to summer visitors.
In the other two cities we've visited so far, Athens and Chania, there are very clear tourist areas. The Plaka in Athens is a mix of streets full of shops, restaurants, bars, gyro stands, and occasional ruins. (There is also an incredible baklava place that sells Nutella baklava - oh man, it's good.) Chania's old city has narrow alleys that lead between gorgeous homes and ruins from both the destruction of the Minoan civilization and World War II bombings. In both cities, the history is present and mingled into the everyday landscape. Naxos does have significant history - I'm not sure how many centuries it goes back, but quite a few - but as you wander through the old market and the old city, you easily find yourself stumbling into residential areas, churches that are still in use, and signs that are only in Greek. There are definitely more touristy areas, but they blend quickly into the everyday physical landscape.
In the other two cities we've visited so far, Athens and Chania, there are very clear tourist areas. The Plaka in Athens is a mix of streets full of shops, restaurants, bars, gyro stands, and occasional ruins. (There is also an incredible baklava place that sells Nutella baklava - oh man, it's good.) Chania's old city has narrow alleys that lead between gorgeous homes and ruins from both the destruction of the Minoan civilization and World War II bombings. In both cities, the history is present and mingled into the everyday landscape. Naxos does have significant history - I'm not sure how many centuries it goes back, but quite a few - but as you wander through the old market and the old city, you easily find yourself stumbling into residential areas, churches that are still in use, and signs that are only in Greek. There are definitely more touristy areas, but they blend quickly into the everyday physical landscape.