In the south part of the island - about 14km from Argostoli, close to Svoronata - you find a sandy beach called "Abythos".
There is no bus line - you need a car or a bike to get there.
Go away from the main part and you will find nudists.
It is not an organized nudist beach.

There is a gay beach called "Peukoulia".
Location: north west of the island, 2km north of the village Agios Nikitas.

And another beach which is named "Gialos", situated close to the village of Athani.
A lot of opportunities for gay cruising.