Having lived in Italy and since I will likely retire there, here are a few of my observations FWIW:
If you could go to either Venice or Florence and you may never get a chance to go to Italy again, Id go to Venice. It is a very unique place. Ive been there seven or eight times and I just dont care for it because of the smell, the cost, and the tourists but Im quasi local in my mind so its different. I definitely prefer Florence but Im not talking about me. Im speaking to people who have never been to Italy.
Florence is also slightly overrated if you are not making a specific cultural tour but Tuscany is not. You can go to San Gimignano, Siena, Montepulciano, Arezzo, and to any of the villages in Tuscany and have much better food, fun, at a reduced cost. You could also go to Tivoli just outside Rome which is probably one of the least appreciated places on the peninsula.
The places I go in Italy are near LAquila in the Apennines, to Rimini in Emilia Romagna, to Bologna, and to Apulia. There are a lot less tourists in those places (except Rimini which is the Ft Lauderdale of Italy) and most of them are significantly less expensive than Florence. If youve already been to Italys major tourist centers try these other places. Bologna is really underrated and it is the cuisine capital of Northern Italy (Naples in the south). Any pasta dish you eat in Bologna will probably be the best youve ever had. Apulia is stunning. Great seafood, nice small seaside towns, its cheap, the folks are friendly, and its really warm in June and September. Otranto is one of my top five locations.
Rome is the greatest city in the world not named New York. There is just so much to see and do that it is overwhelming. To me if you dont spend a week in Rome you will likely not even begin to appreciate it. Really all you have to do is not get a hotel or eat in the high traffic tourist areas and watch your valuables and Rome is a great experience. Take the underground to the tourist centers but stay on the peripheries of the major tourist traps and please, please, please do not eat in the tourist areas.
I lived in Naples for three years so this is one of my favorite places. Sorrento, the Amalfi Coast, Vesuvius, and Capri are must sees. If you really want to have fun in Naples go to the island of Ischia to the spas and ride a motor scooter all day through the narrow roads. Also eat some fish at a restaurant in the inner harbor in Naples and eat pizza as often as you can. They invented pizza in Naples and they do it better there than they do anywhere in the world. Also do some shopping at the various markets because outside of the Florence market, the Naples market is probably the best in Italy. I wouldnt recommend Naples to anyone older people however as you must pay great attention to the pick pockets. In Rome there are more thieves but in Rome they have a decent police presence. In Naples youre on your own outside the main port area. I really, really, really miss Naples.
One last thing is never go to Italy in August. Never! Leave the Italians alone in August and youre vacation will be much more enjoyable.