The coast around Byblos has several beach spots, though the shoreline is mostly rocky rather than sandy. The main appeal is the combination of swimming with spectacular sunset views over the Mediterranean.
Several beach clubs and waterfront restaurants operate along the coast north and south of the old town, offering sun loungers, pools and food. In summer these get busy, especially on weekends. Even in cooler months, the seaside restaurants make a pleasant spot for lunch with a view.
For sandy beaches, you are better off heading south to Tyre or north toward Batroun. But for a swim after exploring the ruins and the old harbour, the rocky coves near Byblos are perfectly fine.