Tips for accommodation for a week

Hey there,

I'm going to Sicily for the first week of the new year. Travelling with my wife and our 7 month old baby daughter. We would like to stay in Palermo for the first couple of days and then go into nature, either beach or mountain.

We understand that January is low season but we are wondering if anyone could give us some tips for accommodations/towns that still have some life around this time of year, and are not entirely closed.

Thanks in advance!