Byblos is a small town and the historic centre is entirely walkable. The archaeological site, the Crusader castle, the old harbour, the souk, and the main restaurants are all within ten minutes' walk of each other. Arriving by taxi or service from Beirut, you'll be dropped near the centre and can cover everything on foot.
The coastal highway that runs through town separates the historic centre from the newer commercial areas to the east. On foot, take care crossing this road — traffic moves fast and pedestrian infrastructure is minimal, as throughout Lebanon.
For exploring further afield — the beaches north of town, or the villages in the surrounding Byblos district — taxis are the practical option. Agree the fare before getting in. During summer, some visitors rent scooters, which are useful for reaching beach clubs along the coast.
There is no public transport within Byblos itself. OCFTC buses pass through on the Beirut–Batroun coastal route and can be flagged down on the main road, but they're not useful for getting around the town.