Current plan is to arrive 7/24 (Fri.) on overnight flight from JFK to Rome (early afternoon) with 3 hour layover in Milan. Staying in Rome until 7/27 (Mon.) when we'll take train to Sorrento for three nights. Train back to Rome for 7/30 (Thurs.) and flight home following day.
Tentative itinerary:
Day 1 (Rome) - check into hotel near Pantheon; walk around (Pantheon, Trevi Fountain, Spanish Steps, etc.)
Day 2 (Rome) - Vatican tour (morning); Borghese Gallery (afternoon)
Day 3 (Rome) - Colisseum, Forum (morning); Open to suggestions (afternoon)
Day 4 (Rome/Sorrento) - Train to Sorrento in morning. Explore Naples. Open to suggestions
Day 5 (Sorrento) - Bus/Ferry day trip down coast to Amalfi and Positano
Day 6 (Sorrento) - Day trip to Capri
Day 7 (Sorrento/Rome) - Stop at Pompei on way back to Rome via train; Arrive Rome mid-afternoon. Open to suggestions
Day 8 (Rome) - Morning flight home

Does this itinerary make sense? I thought about going directly to Sorrento after we arrive in Rome but think we'll be too tired from the overnight flight/layover in Milan. Should I cut a day out of the trip to Sorrento and instead do a day trip from Rome to Florence or Orvieto? The more I read this forum, the more I am having second thoughts about our itinerary. I wish we had more time to explore.

It really depends on your priorities. The Amalfi Coast offers wonderful landscapes (although I'd skip the day trip to Capri; it's hugely overrun by day-tripping tourists and not vastly different from the mainland); Florence and, to a lesser extent Orvieto, offer remarkable art and architecture.

Instead of a day trip to Capri you might find that a day trip to Pompeii is more rewarding. The ruins deserve most of a day; it's a big place requiring a lot of walking.
Otherwise your plan,though crowded. seems doable.

Next to the forum is the Capitoline Museums. You might want to do that on day 3. St. Peter's in Chains is also nearby (just off via Cavour).

Are you staying in the same hotel in Rome on your last night? We've left luggage in the hotels storage room when going to the Amalfi Coast for a few days and shared a smaller bag so we didn't have much luggage to lug around.

What time does your flight arrive in Rome? I would be tempted to train (or bus - there's one at 3 pm) on to Sorrento that day.

KyBourbon, we are staying at the same hotel in Rome. You suggestion of leaving one of our bags there is a great idea. Never would have thought to do that. We arrive in Milan at 8:50 am, leave Milan at 12:40 and arrive in Rome at 1:50 pm. We will have cleared customs in Milan.

I would pop for 300E and hire a driver from FCO to Sorrento and start there. Why stay in Rome twice? And,relax on the coast from the start---Rome can be hectic.

Bob,I thought of doing as you suggested but I can't justify the expense. I'm concerned that we will be too tired to take the train on arrival in Rome to Sorrento. Unfortunately, I wasn't able to find a cost effective flight directly into Naples from JFK.