I'm just back from a 2-week vacation in Italy. Oh boy there are things to be said about Italy!
Things to know before going there
First off, a few warnings! Roada are race tracks for italians. On the freeway, when they want to take over, they drive as closely as possible behind, occasionally doing headlight flashing. Also, still on freeways, speed limit can drastically change from 130 to 60 in no time where there's road work, and no one seems to pay attention, they barely decrease their speed to 110. Oddly enough though, I saw a shit ton of electronic speed radars.
In cities, anywhere where there's asphalt, cars and scooters will go. Even in the narrowest streets. Don't you dare try to follow what Google Maps says, stick to the wide main roads. Italians mostly drive two kinds of cars: either tiny ones like Smarts, or SUVs. Also, a lot of them just don't give a shit about seatbelts. They'd rather hear the sound that reminds them to fasten it for 10 minutes than actually fasten it (I experienced several car rides with italians in Naples!).
I was shocked by the number of smokers. It's by far worse than in France. People smoke everywhere: train stations (apparently it was not forbidden), houses, and I even saw a bunch a young people smoke in trains (it is forbidden but no ones seems to care). Speaking of trains, there are unreliable. Expect most of them to be between 5 and 10 minutes late all the time.
The density of traffic in cities is incredible. Cars and scooters are everywhere, and pollution must be a serious concern. It smells like gas everywhere. It is not uncommon to find roads with 4 or 6 lanes (2x3) in cities, so no wonder why it's so polluted. Also be prepared to hear horn hooking all the time. I also saw scooters parked on the rightmost lane (not a parking spot at all) alongside the sidewalk, crazy! Likewise, Smarts park perpendicularly to the sidewalks.
Helmets for scooter drivers was made mandatory in 2005 or something, but I've seen numerous people without one. Also, at red traffic lights, if there are 3 lanes, italians are gonna make 5 out of them, haha! It saw that in Rome many times.
Public transportation seems to be poorly developed. Even Rome has only 3 metro lines. Trains coming from the suburbs to Naples run once an hour, so plan in advance.
The garbage collection system is also not ideal. It is not uncommon at all to see overfilled street collectors.
Last funny fact: the water tank of toilets is... unusually located.
Now, let's move on to cities.
Cinque Terre is meant to be visited by train or hiking, forget about your car as the roads are narrow, steep, with series of switchbacks. Trains run every 20mins or something between the 5 villages, and the day ticket costs 16 euros. Hiking takes a full day at a relaxed pace (6+ hours).
There is not much to do in Pisa, appart from the leaning tower of course. The city center is very beautiful, a lot of streets are car-free, with tons of pedestrians and cyclists. I recommend discovering the city on a bike.
I highly recommend doing guided tours, as opposed to solo tours, especially when visiting the Vatican museums, the Colosseum and the Roman forum.
Don't buy city passes, it's in most cases cheaper to buy tickets individually.
If you're on a tight schedule as I was, I found this map very helpful when it comes to visiting main highlights efficiently.
Funny fact: every night, there are fireworks in the city, usually between 22h and midnight. I asked why and was told that it's to celebrate weddings, parties, etc... anything that's worth celebrating. Regular people do that.
When visiting Pompei, do a guided tour! You'll find plenty just as you walk out of the train station. The one I did was 12 euros per adult for a 2-hour group tour. Official guided tours, located just by the ticket office, were 2 euros more expensive if my memory serves well.
The city of Naples is not very interesting as it is. I recommend spending a day in the city, not more. Make sure to eat the best pizza in town at Gino e Toto Sorbillo. Then, you can visit Mount Vesuvius (reachable by car!), Pompei (train is the most efficent and cheapest way to get there), Sorrento (same train as Pompei) or Capri (take a ferry, it's a 40-ish euro ticket for both way).
That's it! Hope it helps.