The ancient city near Tunis that was once the capital of the Carthaginian Empire is Carthage.
Carthage was founded on the eastern side of the Lake of Tunis and developed from a Phoenician settlement into the capital of a powerful Punic empire. Its location gave it access to major Mediterranean trade routes, helping the city become one of the ancient world’s richest commercial and naval centres.
The city is traditionally linked with Queen Dido, also called Elissa, who was said to have fled Tyre and founded Carthage. The famous oxhide story belongs to this foundation legend, not to a securely documented historical account. Carthage later challenged Rome for control of the western Mediterranean, most famously during the Punic Wars.
Rome destroyed Punic Carthage after the Third Punic War in 146 BC. A Roman city was later built on the same site and grew into a major centre of Roman North Africa. The archaeological site lies about 15 kilometres northeast of Tunis and includes remains from Punic, Roman, and later periods. Nearby Utica was a rival city, but it was not the former capital identified in the question.