The northern walls of Tarragona's old town are not medieval — they are late Republican Roman, built between 218 and 197 BC and among the oldest surviving Roman fortifications in the world. The walls were built on top of much earlier megalithic Iberian foundations, which you can still see at the base — massive irregular blocks weighing several tonnes each, predating the Romans by centuries.
The Passeig Arqueològic, a paved path between the inner Roman walls and the outer 18th-century walls, makes for the best 30-minute walk in Tarragona. The path is shaded with cypresses, scattered with carved Roman inscriptions and statuary, and offers views over the old town. Enter from the Portal del Roser at the western end or from the bishop's palace at the eastern end.