In The Leopard, Di Lampedusa's prince observes that Sicily was the America of the ancient Greeks: a nearly empty land with some easily vanquished tribes, where they could found major cities and expand their civilization.
Major pre-Greek cities included Selinunte, which eventually became Greek, adopted Greek religion, and developed Greek ways. The Punic wars between Carthage and the ancient Greeks and Romans were fought to dominate Mediterranean ship traffic: Sicily is very close to Europe, and spans the narrowest portion of the Mediterranean; Carthage was close to the point across from Sicily. Until the end of the Middle Ages, ships hugged the shore; this was especially true in ancient times -- look what happened to Odysseus whenever he was blown off course and into the wine-dark sea!
Because Selinunte was destroyed in one of the later Punic wars and then forgotten, it's a magnificent source of archaic Greek and even pre-Greek art and architecture. These friezes from one of the main temples there were collected in the 19th century and brought to the museum in Palermo (a typical 19th century thing to do: take the art work away from the site -- lucky it isn't in Rome or London!) Greek mythological themes are easily recognizeable: I have selected just a few images.
The city itself has a full acropolis, including a theater, marketplace, and many other civic buildings, and a vast, open-roofed temple, which we visited on an earlier trip. The lion-head water spouts from the temple and a vast grotesque face are the most impressive items in the collection. Numerous vases, oil lamps, clay and bronze statues, figures from ancient Greek and pre-Greek graves, and other items from Selinunte and elsewhere are also on display in the museum.
Shipwrecks preserved much evidence of art and technology from ancient times as well: the first helmet, below, obviously spent millenia at the bottom of the sea. The museum also claims the world's largest collection of ancient anchors. These are made from stone and bronze or iron, and are on display all around the courtyard of the museum.