In October, weather is iffy in the Cinque Terre, and when the weather's bad, you won't want to be there. I'd spend a little more time elsewhere and save that for your next trip. Once you've been to Italy, you'll be back!
I'd rather stay in one place and day trip, so I'd choose Sorrento for the south since it has the best transportation connections to the rest of the area: local (Circumvesuviana) train to Pompeii, Herculaneum and Naples, buses and ferries to the Amalfi coast towns and ferries to Capri.
Then I'd stay in Florence and day trip to Siena and other Tuscan towns by bus or train.
I like the suggestion of starting in the south, then flying from Naples to Venice and working your way back to Rome. Venice is so much better in the mornings and evenings after the day trippers have gone.