Favignana is definitely worth a visit. You can rent a bike and spent the rest of the day cycling from one beautiful place to another. Take a dip in the azure bays and imagine yourself in paradise.
Book up in advance you ticket for the boat (usticalines.it) from Trapani. The boat trip takes only half an hour.
Ustica is a small island about 70 km north of Palermo, from which it can also be reached. It is a getaway for walkers and snorkelers, so do not forget your snorkel!