Founded by Phoenicians and home of Hannibal, Carthage was one of the greatest cities of the ancient world. The site retains its natural splendour, with lush vegetation and superb views over the gulf. Highlights are the museum and excavated quarter atop Byrsa Hill, the Antonine baths, the Punic ports, the Roman amphitheatre and the Sanctuary of Tophet.
Despite Carthage's fascinating history and the position of dominance it held in the ancient world, the Romans did such a thorough job demolishing it that the ruins today are something of a disappointment. Most of what remains is of Roman origin. There are six main sights, and the hassle for visitors is that they're spread out over a wide area. To overcome this, hop on the TGM (light rail) line that runs through the middle of the area, but be forewarned: it'll still require a fair amount of hoofing it.
The best place to start is Byrsa Hill, which dominates the area and gives a good view of the whole site from its peak. At its base is the L'Acropolium (Cathedral of St Louis), which is visible for miles around... and is an eyesore of massive proportions. It was built by the French in 1890 and dedicated to the 13th-century saint-king who died on the shores of Carthage in 1270 during the ill-fated 8th Crusade. Though it was deconsecrated and closed for years, its has now been restored and is open to the public. The National Museum is the large white building at the back of the cathedral, and its recently revamped displays are well worth a look. The Punic displays upstairs are especially good.
The Roman amphitheatre on the west side of the Byrsa, a 15-minute walk from the museum, is said to have been one of the largest in the Empire, though little of its grandeur remains today; most of its stones were pinched for other building projects in later centuries. The collection of huge cisterns northeast of the amphitheatre were the main water supply for Carthage during the Roman era - they're now ruined and hardly worth the scramble through prickly pear cactus.
The Antonine Baths are right down on the waterfront and are impressive more for their size and location than for anything else. The Magon Quarter is another archaeological park near the water, a few blocks south of the baths. Recent excavations have revealed an interesting residential area.
The chilling Sanctuary of Tophet created a great deal of excitement when it was first excavated in 1921 and has gone on to elicit a fair amount of 'excited' prose since then. The Tophet was a sacrificial site with an associated burial ground, where the children of Carthaginian nobles were killed and roasted to appease the deities Baal Hammon and Tanit.