The main ancient monument in Lebanon is, of course, Baalbek. The temple of Bacchus is bigger and better preserved than the Parthenon in Athens; the temple of Baal-Zeus-Jupiter next to it must have been one of the largest shrines of the ancient world (after the Egyptian temples, of course).
Beirut is a very modern city, which is currently being rebuilt, so don’t expect too much of the ancient ruins. This is the place to be if you like modern architecture. Still, it has two of the best museums in the Middle East: the National Museum and the Archaeological Museum of the American University.
We loved the Roman ruins of Faqra and Machnaqa, but were unable to visit Yanouh, Afqa, and Sfiré. The Roman temples at Niha were splendid – do not forget to go into the cellar of the great temple.
To the north, there is Byblus, which has been inhabited for thousands of years. You can see Neolithic and Chalcolithic buildings, temples from the Bronze Age, Phoenician royal tombs, a Persian terrace, Greek and Roman structures, a mosque, a perfectly preserved Crusader castle and ditto church, and so on. If you go up north from Beirut, do not forget to visit the reliefs at the Nahr al-Kalb, where about every army has left an inscription – from Ramesses II to the Lebanese army that forced out the Israeli troops in 2000.
I really loved Tyre, which offers two big excavations. At Al-Bass, there’s a hippodrome and a large necropolis, while at Al-Mina, you will see the remains of the city itself. Here are also the remains of a Crusader church, which is more or less on the place of the ancient temple of Melqart.
This was only a selection. If you want to see all sights mentioned by Guillaume Gernez and Ingrid Périssé-Valéro, you will need about two weeks.