Balaklava is a former home of Soviet nuclear submarines, but now it is merely a small colorful port full of tourist vessels (but you can still check out the natural submerged cave where submarines were located).
You can go by scheduled boats and then hike to a remote beach; or you could just rent a smaller boat that would bring you directly to one of the numerous secluded spots to the south of Balaklava.
There is a dry pine forest, and small pebble are beaches squeezed between the rocks. We went there just for a day, but apparently it is very popular for camping. Nudity is a commonplace.
On the way back, my sister and I saw a bunch of guys covered in grey mud, but it didn’t occur to me to take a photo, although they were posing like statues. I guess I’ll have to return there!