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It is worth noting that according to UNESCO, there is only one known site containing the remains of a Carthaginian city: Kerkuane, in Tunisia.
This Phoenician city was probably abandoned during the First Punic War (c. 250 B.C.) and as a result was not rebuilt by the Romans. The remains constitute the only example of a Phoenicio-Punic city to have survived. The houses were built to a standard plan in accordance with a sophisticated notion of town planning.
There are many significant archeological sites in North Africa that had their beginnings as Phoenician settlements; Leptis Magna and Samartha were originally Phoenician trading colonies, and they (along with Carthage itself) are World Heritage sites as well. But most of them were later built over by the Romans, and their Punic heritage is no longer very evident.
It is possible that there are isolated Carthaginian ruins that survive in Libya; isolated Carthaginian sites do exist elsewhere (e.g., the Punic wall of Cartagena, in Spain.) However, if you're hoping to find something on the scale of the major Roman ruins that still exist throughout the Mediterranean, Kerkuane appears to be all there is.