You could try the Black Sea coast, where very few foreign tourists go. Probably the most beautiful resort is Amasra, a collection of red-roofed houses on a tiny rocky peninsula, backed by steep green hills. It is not a big resort (the geography limits its size) and is only really popular with Turks from Ankara and Istanbul. There are no big hotels, just lots of small pansiyons which are family-run B&Bs.
There is a beach in town which isn’t bad, but a couple of kilometres along the coast is Bozkoy where there is a great white sand beach, almost deserted save for a couple of small beach cafes. There are minibuses (dolmus) from Amasra throughout the day in the summer.
Nearby, you can visit Safranbolu, which is a really beautiful town about an hour inland…hundreds of old Ottoman houses in a valley.
Maybe the reason why it is not popular with foreigners is that Amasra is not that easy to reach. The nearest airport is Istanbul, about 7-8 hours by bus…but then you have the excuse to spend a couple of days in that city!
Another reason is that the weather on the Black Sea coast isn’t as reliable as the other Turkish coasts…it rains a lot more, but summer weather is usually better.
A couple of links:
Pictures and info about Amasra:
Might not be exactly what you’re looking for, but if you want a completely Turkish resort, Amasra is a good one :@P