I feel like people bag on Rome. Not here. Just in general. If you've never been to Italy, and you are even halfway interested in history, Rome is the most fascinating city on the planet.
They have 2000 year old buildings on every block. The touristy shit is incredible. Forum, Coloseum, Trevi fountain, Pantheon, Vatican City, etc etc. And just stop in random places to rest and have a bottle of wine and a bite. The piazza by the Pantheon is a total tourist trap, but one of the best people-watching places I've ever been. I distinctly remember the red wine and pizza my wife and I had on our first trip. We spent an hour just basking in the sun and scenery.
Food in Rome is underrated as well. Gelato and cacio e pepe will be staples for your kids.
With 4 days in Rome, I might recommend doing a day trip to Pompei. Are you renting a car? It's a fairly easy drive, and it is amazing. Or save for your next trip. Because nobody can do Italy once.
Do not skip seeing David in Florence. I'm not an arts guy, but that was the highlight of Florence to me. If you have 3 days, you have time to do a day trip to one of the Tuscan towns nearby.
Never been to Venice. Jealous
Nor Cinque Terre. But I have done Amalfi. Same trip as Pompei. God that was a great 5 days.