Just finished a 6-day trip to Italy 3 weeks ago. Day 1 - Milan, Day 2,3 - Verona, Day 4 - Florence, Day 5,6 - Rome.

I agree with others that you should concentrate on two cities - too much moving of luggage and travelling is a pain.

You could spend weeks in Rome and not see half. Plus, I think the variety is better - museums, Vatican City, ancient ruins, etc.

If you don't mind the AirBNB route, we stayed at this place and it was well located, very friendly hosts and reasonably priced: https://www.airbnb.com/rooms/835940

We loved Verona and the variety of things to see (castle, arena, theater, shopping) is very good.

I think the advice to skip Milan is good as well. The Duomo and shopping is fantastic but other cities are going to give you a more enjoyable experience I think.

If you book train travel, don't use Rail Europe, book directly through Trenitalia or another rail service.

Good luck with your trip!