If I understand this correctly, you are saying that you have 13 days to spend in Italy with a completely open agenda. The only thing that you are leaning towards is that you have friends who once stayed at an apartment in Livorno, and you are inclined to see the hill towns of northern Italy. If that's the case, you have a lot of options.
I would not blow off Venice as a side trip. Venice is not a side trip. It is a destination. With an October visit you'd actually be able to get to Venice pretty close to the perfect time to visit one of the most unique and most beautiful cities in the world.
Last edited by Perche; Jul 16, 2014 at 2:57 pm