The Punic Wall is the place to start if you want Cartagena before Rome. The archaeological site preserves part of the 3rd-century BC defensive wall of Qart Hadasht, the Carthaginian stronghold that gave the city its strategic importance.
The remains are modest compared with the Roman Theatre, but the interpretation is useful and the history is tremendous. It helps you see Cartagena not just as a Roman city but as one of the great prizes of the western Mediterranean.