Have spent a lot of time in Italy.
Use the same sense you'd use in New York, Chicago or San Francisco and you should be fine.

I've been ripped off once in Italy, and it was the official ticketseller at the train station, routinely giving bad change (we caught him at it the second time)

I don't expect you'll find many opportunities to ride in Rome and Sorrento, but near Florence you might have better luck. I have no experience in Venice.

It helps to look and act like a native. Italian women rarely wear shorts or bold prints or white sneakers for example.

Learn some Italian. Italians love to hear us try.

but yes, there are thiefs in Italy, as well as pickpockets. My husband carried his wallet in his front pants pocket instead of the rear pocket, and don't leave your camera sitting on a table ignored, you know, common sense stuff.
As for day trips, you're going to be so busy in each of those cities that a day trip probably won't be necessary.