I have been to both Sicily and Malta. In the summer time, you need 1 week in both. However as you are going in January which is out of season, you can do 1 week in both.

In Malta you need at least 1 day to visit the old town of Valetta and also the old town of Medina, about 20 minutes away is not to be missed.

Try to have dinner or lunch at the Xara Palace Hotel in Medina. A fantastic view and wonderful food in an old palace.

Also you need a day to go to the island of Gozo. Also a must see. Takes about 1 to 2 hours by taxi and boat.

In Sicily I would stay in Taormina. Beautiful hilltop village. You can take a day tour to Mt. Etna from there. In the summer Mt. Etna is really cold so in the winter must be freezing.

Hotels in Malta are the Hilton which is very nice. Also the Westin which is cheaper. There is an old one next to the old town of Valetta. Forgot the name.

In Taormina my favorite is the Villa Diodoro. Beautiful views of Mt Etna and well located in the village. Go to Tripadvisor.com. Great site for hotel reviews.