Thanks for all of the suggestions.
Yes we have 13 days and no real agenda. My wife likes cooler weather and small towns. She is not real keen on large cities. She likes water. Hence why we were looking at the coast and Lake Como. Livorno was only mentioned because our friends stayed near there in an apartment for a week. We are in no way tied to that area.
What we normally like is to stay away from large touristy areas.
This trip we were thinking it would be preferable to park ourselves in just a couple of spots and use them as bases to do day trips. I am open to other ideas.