When I asked this question on another forum, asking people's favorite
anchorages on the South Coast of
England, I got a few answers to the effect of -- if I told you, these places would get more crowded, so [buzz] off. Followed some time later by lots of very helpful suggestions.
But we are much friendlier around here.
My favorite place in the area you are talking about, and maybe my favorite anchorage anywhere, is Knidos, at the tip of the Dacha peninsula. Don't miss it.
But as others have said, the whole coast is incredibly beautiful, and besides that easy to sail (you don't need a chart plotter, and hardly need a
depth sounder -- navigate and pilot by sight, there are almost no hazards).
The only disappointment I had was getting run out of Palamut by unwelcoming local fishemen when I tried to take refuge in a storm; ended up spending a sleepless night anchored off a lee shore in open
water in a blow.
If you go a little further around, there are many joys in the Bay of Gokova, starting, of course, with lovely Bodrum. Don't miss the dramatic bay of Akbuk, if you get that far, lined with tall mountains and nearly empty all the time. The tourist trap of Cleopatra's Island is worth a miss, at least in summer when it full of tripper
boats 24/7.
P.S. Some of the places mentioned by the previous poster are in
Greece -- Simi and Rhodes, for example. It is a huge PITA to clear out of
Turkey and into
Greece, and not worth it if you are only on a week or two
cruise, IMHO.