Help with itinerary

This July? Good news, that is a luxurious amount of time. Bad news, many places book up months in advance on the coast in particular. I would go directly to Booking.com to do an accommodation search by what is available. All reviews there are verified.

You will get very far with specific questions, for now focus on accommodations. Do you have a list of what you want to see in each place? Your interests should dictate how much time in each place, but four nights to a week in each place is a good estimate.

My trips are normally 2 weeks and I always am in and out of Rome, so I go immediately south to Salerno (which you could do for the Amalfi Coast) to do my time there first, then I go WAY north and make my way back down to Rome and end there before my flight out. One less hotel change (if you're already on the move, extending it a few hours shouldn't be TOO hard to reach the coast) and ending in your departure city.

I would look into attractions in each place and see what YOU want to do. Then make hypothetical day plans to see where you want to devote most of your time. It's awesome that you have so much time!

When the train tickets go on sale (after you have decided how to split your time) in June, you can save money by buying in advance (don't bother doing it for your arrival, it is easier to buy the "next" train when you get through all the rigamarole at the airport).

We definitely want to see the major sites in Rome such as St. Peter’s Basilica, Vatican museum, Trevi fountain,, Sistine Chapel, Pompeii, Sorrento, Capri, Florence. We don’t want to be on the go the entire time. We would like some relaxation time on the coast since it will be hot.

Oops I meant we arrive July 25 on a red eye and return August 2.

oh wow...then that's a week.....that might not work like...at all....I would pick two places at the MOST, as moving locations takes a lot of time, at LEAST half a day and usually you're not able to do much at all that transit day and you don't want to waste time. Still, go the farthest away and come back to Rome, and since your flights are in and out of Rome, that is one of your cities. You get to pick one more :)

So you have 8 nights. I would spend the first 4 on the coast and the last 4 in Rome with a daytrip to Florence.

Ooooo I like Joyce's idea :)

Yep, gotta scale way back to one or two places.
I'd let accommodations guide you as to your selection. I'd rather wait on the AC than do it in a subpar location in the heat of late July. Plus with limited time I would not want to spend it in transit.