We visited Rome for a week and managed to see the major sites and several others that we just stumbled upon. We know we missed a whole lot and plan to return again this year to go more in depth. I don't think you will regret spending the whole week there.
Here are images of our trip. There is lots to see.
Rome http://www.flickr.com/photos/stanbr5...7634677664021/

First, if you're going to spend 7 days, my preference would be for an apartment. I'm an apartment person anyway, but I particularly like staying in one when you're in a big city that has a lot of hustle, bustle and noise. It's nice to have a place where you can stretch out and take a break. If you have a nice view or a balcony, all the better. For me, hotel rooms don't do it.

Your friends who tell you it would be a "waste" to stay in one place may be the types who try to pack in the most sites in the shortest amount of time. To each his own.

Your husband's family is from the Amalfi Coast. It's July.

To me, this speaks for itself: split the time between Rome and an AC town.

If you're staying in Rome, in July, I suggest getting the nicest hotel with the best rated air conditioning you can afford. I wouldn't use this as a time for budget rooms. And I would use taxis.

Well, I've been three times to Rome - 5 nights, then 7 nights then 8 nights. See the trend - I spend more time each time rather tha less!
Rome is incredible and the riches go deep (lierally, each of the days I've spent in Rome, I went underground somewhere...and each time to a different underground site). The churches are full of art. The museums have fantastic collections and some of those smaller museums have limited opening hours so the more days you are there, the easier it will be to schedule a visit. I could easily spend several months in Rome without missing my beloved NYC! The people are friendly and the food is very good. It is easy to go off the beaten path and spend time in "real" Roman neighborhoods (and still visit historical or artistic sites since there is great stuff to see no matter where you find yourself). I haven't visited in July and I'm sure it's hot, hot, hot so you'll likely be moving slowly and have days that are not quite as full as they would be in cooler weather. IMHO, all the more reason to stay the full 7 days.

Pantheon, Trevi, Navona, Various Churches, Spanish Steps - 1 day
St Peters and Vatican Museum - 1 day
Colosseum, Forum and Capitoline Museum - 1 day
Vittorio Emmanuel, St Peter in Chains, St Maria Maggiorre - 1 day
Villa Borghese and Catacombs - 1 day
Anzio - 3/4 to 1 day
Ostia - 3/4 to 1 Day
Trastevere and Campo - 1 day
Pompeii - 1 LONG day
etc

bottom line - we spent 5 days on our first trip and 14 on our second. 7 is not too many at all!

I would split it up between Rome and the Bay of Naples--Sorrento isn't really the Amalfi Coast, but it's close enough and you can get to Naples (a couple of really great museums there) Capri, Pompeii and the AC easily from there.

Rome is my spouse's favorite city in the world, it is not mine and if I were in Italy for the first time, I wouldn't spend all my time there.

here's another Rome fan.

I never went there until li was 50 and since then i've been trying to make up for lost time.

the great thing about day trips is that really you don't need to make your mind up until you get there. so have a few ideas [plenty here] in case you want a break from the hurley burley, but plan for spending most time in Rome.

You won't run out of things to do!

Thank you so much for all the responses! You guys have given us a wealth of information.

We from the Southern United States were summers are 100 degrees in the shade with outrageous humidity and we barely turn on our A/C so perhaps a summer in Rome is right up our alley.

Is Naples really close enough to attempt?

Naples is an easy day trip from Rome; the fast trains take little more than an hour to get there. However, it's a big city, so of course you wouldn't see much of it in one day.