Palermo is a 45 minutes drive away. There you can spend hours getting lost in the small streets, sniff the smells of local delicacies, stroll around the many markets or visit museums.
A few attractions in Palermo are:
From Palermo you can also take a boat to the island Ustica.
Trapani is located on the west coast of Sicily. While you are there, go and visit the salt mills, take a stroll through the shopping streets. Here you can take the boat to the Egadi Islands Favignana, Levanzo and Marettimo.