Just saw you’re not planning on driving a rental car, so that could change things. Still, we had 2 weeks at Christmastime in 2012, and went to many of the places Rick’s Tour will visit. The tour goes to Erice for a good part of a day, but it’s so wonderful that you could go there before the tour, too. If we’d had more time, we would’ve gone to Cefalù and islands north of the northeast part of Sicily, but haven’t been yet, so no personal recommendations.
If you’re interested in Ancient Greek sites, you’ll visit Segesta and Agrigento temples, but there’s also Selinunte and Morgantina. The latter is reachable if you stay in Caltagirone, a town worth visiting, too.
Then there’s Modica, a paradise for chocolate in the lower town, and a beautiful upper town.
We spent Christmas Eve and day at the agriturismo featured in Rick’s video from more than 20 years ago, and you could do that, too, but would need a car or driver to get you there.