Salammbô by Gustave Flaubert (1862) is the great 19th-century novel of Punic Carthage — a vast, lush, deliberately exotic reconstruction of the Mercenary War of 240-237 BC, drenched in violence, religion, and architectural detail. Flaubert spent five years researching it (he visited the ruins himself in 1858) and it remains the single most influential work of fiction set in Carthage. Some of the descriptions of the Tophet and the Punic Ports will linger in your imagination long after you visit the actual sites.
Carthage Must Be Destroyed by Richard Miles (2010) is the best modern single-volume history of Punic Carthage in English — substantial, accessible, and built around an interesting central thesis: that the Romans deliberately destroyed Carthaginian culture so thoroughly that we know the city primarily through the words of its enemies. Reading it before visiting fundamentally changes what you see.
Confessions by Augustine of Hippo. Augustine studied in Carthage as a young man in the 370s AD and writes about the city memorably — its theatres, its baths, its sexual life, its religious tensions. The North African chapters of the Confessions give you the late-Roman Carthage in the protagonist's own words.
A History of My Times by Polybius is the contemporary account by a Greek who was present in the Roman camp during the final destruction of Punic Carthage in 146 BC. Book XXXVI is essential for anyone interested in what really happened during the siege.