Libya and the ancient world
Unlike today Libya played a major role in the ancient world. In addition to its function as granary of the Roman Empire, it possessed one of the most important commercial harbors (Tripolis) for exotic goods from Africa at this time.
Both the Phoenician, the Greek and especially the Romans left marks. Furthermore the Garamant Empire, of which still very little is known, is said to have made its impact in large part in this region. I recommend those places, which, in my opinion, belong to the most important evidence of the past. There are plenty of books and websites with abundantly information on this subject.
In brief I would therefore recommend in this place:
1) Leptis Magna
5) Al Bayda