I have done the Marmaris to Kekova Roads stretch out of Gocek in Southern Turkey in July this summer. Fethiye bay (Skopea Limani) was very pleasant with light thermal winds and many safe anchorages around. Fortunately there was no heat or mosquito biting problem. I have put the following two video clips in Youtube:
I last sailed in the Ionian in 2004. The winds were also light and the islands south of Lefkas (Meganissi, Kastos, Kalamos, Cephallonia and Ithaki) very picturesque and quiet.
I have been in Dubrovnik many-many years ago and still remember the nice old walled city. In the Adriatic, the sea water is colder than in the Ionian and the area is invaded by swarms of german speaking tourists. Watch out for the BORA, the equivalent of the notorious meltemi wind in Greek and Turkish waters, maybe more unpredictable and dangerous.
The Balearics are known for their strong winds during the summer. British people love this sailing area.
Strangely, you don't ask information about the most challenging and interesting sailing ground in the Mediterranean: the islands in the central Aegean Sea. Are you a fair weather sailor or what?