My guess is that you haven't been to Venice; if you had, you wouldn't want to day trip there. Why not start in Venice (2-3N)? It's low key - even in tourist season you can wander the back canals which are very charming and full of interesting things to see and do - and enjoy the most popular areas, the Rialto Bridge, Piazza San Marco, and the Grand Canal in the early mornings and evenings, when the day-trippers have gone. You can see the sights of Bologna in one day. You have options: leave Venice very early, check bags at the train station, spend the day in Bologna and continue to Florence; or day trip from Florence; or spend 1N in Bologna. 5N in Florence sounds like a lot. Siena is a good day trip by bus.
For the "south" where you stay depends mostly on what you want to see and do in the area. Sorrento is kind of a PITA to get to/from. It is a good base if you want to go to Pompeii, Herculaneum, Capri. It's not quite as good for the Amalfi Coast and there's not much to see and do in Sorrento itself. If you want to spend your time on the AC, Salerno may be a better choice, with good bus and ferry service to the AC towns and high-speed trains to Naples and Florence.
I spent 5 nights in Naples in February last year. As Harold has often said, the only sublte thing about Naples is its charm. I am a retired woman and traveled solo. I found Naples to be safe, though there were a couple places that I walked through feeling a little uneasy, but the only time I was in any real danger was crossing the street. Traffic is crazy and middle of the street is safer than corners (yes, even with traffic lights), because at least in the middle of the street, you can see everything that's coming. Naples is a little grittier, a little poorer, and a lot more in-your-face than other places, north or south. If you approach it with the right state of mind, it's a very good place to stay, unless you want to see the Amalfi Coast.