If you find big pebbles uncomfy, then use the wooden platforms by the old jetty or walk over it to the patch of sand on its left side. Here there's a few palm trees, a bar, and the best view of the west coast cliffs. Don't try and walk round to the remnants of the Finger of God ock: The cliff is unstable.
Another pebble.-free alternative just north of the harbour is the natural swimming pool complete with lava arches and great sunset views.