I would not be surprised to learn that the Phoenicians settled all around the Mediterranean especially Sicily and Libya.
Of course it has always been known they came from the area of Lebanon. Tyre and Sidon for example.
The spread out, including Carthage of course, which rose to prominence and dominance over the home cities, eventually fighting over and conquering most of Sicily at the expense of other Phoenicians, and Greeks and whomever else was around. They had good trade relations with other Greek and Etruscan cities in the western Med, colonized along the western Atlantic coast of Africa, and circumnavigated Africa for the Egyptian pharaoh, starting in the Gulf of Suez (probably) and sailing clockwise, winding up at Gibraltar and eventually the Nile ports.