If you imagine this spot before the sun-worshipers and cafés, it's easy to believe that it was the place where the Sirens lured Ulysses.
The little harbor on the south coast gets the most sun and is protected from the winds by steep cliffs, so it's often warm enough for sunbathing even in the winter.
Take the bus from Capri town or walk down Via Krupp, continuing down the steps from the little church of Sant'Andrea to find the free beaches of Marina di Pennauro and Marina di Mulo.