I have been to the Naples, Almfi Coast, Sorrento, Florence, and Rome. You're going during prime tourist time, Rome will be awful. There is so much to see there 3 days will be hard to get it all in, especially with how packed it will be. It will be hot out so planned accordingly.
Almfi, Sorrento, and Florence are hands down my favorite places. Be careful about Rome and all the "Real Italian food" shit you can get on the streets. The best stuff is down the back roads and off the main drags. I used TripAdvisor for a lot of recommendations when I went out. I visited Rome in December of 17' and it was perfect. 60 degrees and no tourists. I went back again in September, awful. So be prepared for that.
Must do's. That's debatable on what you find important.
Florence we did a city center tour and then a vineyard tour. Ponte Vecchio being a must in Florence.
Rome. Pantheon, Colosseum, Spanish Steps, etc.
Naples. Vesuvius