Paphos itself is not a great beach town — the seafront below Kato Paphos is rocky in places, and the public beach east of the harbour is functional rather than beautiful. For real swimming, head out of town.
Coral Bay, 10 kilometres north, is the headline beach — a wide crescent of sand with calm shelving water and a strip of beach bars behind. It gets crowded in summer.
Geroskipou municipal beach, just east of the town, has dark sand and gentler waves, broken up by groynes; pleasant, but lined with hotels.
Lara Bay, an hour north on the Akamas peninsula, is wild and undeveloped — green turtles nest here. A 4x4 is useful for the final stretch of dirt road.
Further on, the coves around the Baths of Aphrodite and the rough sea cliffs of the western Akamas are the most spectacular, but you have to work for them: walking trails, no facilities.