I've not yet been quite able to spend Christmas in Sicily, but I cannot think of a better place to do it! They're much more religious there, and thus you'll see more "Real Christmas" things. I have good friends who live in Taormina (on the West side of Sicily) and every year I see beautiful pictures of the Piazza, parades, Christmas Trees and celebrations that they post on Facebook, and it seems the entire town is on the square!
If you're planning on spending Christmas Eve/Day in Palermo, the best way to get an answer to the meals question is to ask the Hotel. I stay in Centrale Palace hotel in Palermo, and they have two dining rooms. I'm sure some restaurants wil be closed, but any place on Earth (including Rome) that has tourists has restaurants open on Christmas. You just need to find out which ones and make a reservation from the U.S. to make sure you're one of the lucky ones.
I was in Rome for Easter, and near the tourist sites (including the Vatican) all the restaurants were open for business, with the exception of the smaller Mom n Pop places.
If you're flexible and would like to consider Taormina, I can give you more specific info. You can PM me.