Itinerary advice - 13 days in Italy - late July

Wow! You got a lot planned in those days. Remember, each travel day is basically a lost vacation day but it can be done if you plan well! I know it would make for a long 1st day, but have you thought of going to Florence right away? It's a short, comfortable ride on the Frecce express train. You don't say what time 'evening' is, but if you look at train schedules you might be able to get to Florence in time for a leisurely dinner and a good night's sleep. Florence really does take more than a day even if you make specific reservations at the sites you really want to take in. I don't know anything about agriturismos, I usually rent an apartment in the cities. Near Florence you might like Lucca and especially Siena. Heading south from Florence you'd take the train to Rome and then onto Naples (probably no change of train). For me, Sorrento is my go-to place and especially the hotel il Nido. Very comfortable, very reasonable and fast becoming known for having the best restaurant in Sorrento. The risotto with gorganzolo cheese and pears is my annual first night's meal. You can do Pompeii from Sorrento easily. It's also the starting point for the Amalfi Coast. My suggestion would be to take the boat from Sorrento to Positano and on to Amalfi town then take the bus back. You get the best views and, on the way back, you won't have to fight for a seat - just make sure you sit on the driver's side for the best views. Food in Sorrento - definitely on the water at Marina Grande; Bufalito; L'antinca Trattoria; da Gigino. Drinks at the Foreigner's Club (food is lousy) overlooking the bay. In Rome, which I would save for last, I always rent an apartment - good chance to do laundry, spread out while repacking, try the local markets and be a Roman for a few days. The Piazza Navona area has plenty of apartments (I use vrbo.com). For food, I've become enamored with the local favorites in Trastevere. Honest food, welcoming people and a fun night out. Enjoy your trip! Maybe we'll run into each other in Rome!

Hi,

While I cannot comment on Florence, Tuscany, nor Sorrento, I would suggest that you consider a stay in Salerno for the Amalfi Coast. The crowds will be considerably less than you would experience staying in Positano, Amalfi Town, etc. You can get to Pompeii from Salerno also if you wanted to choose that over Naples. We loved the calm, authentic feel of Salerno.

I explain visiting Pompeii, Positano, and some other interesting sites in the area in this post: https://community.ricksteves.com/travel-forum/trip-reports/salerno-67b65651-b7f1-43eb-a5c0-b9b56c5c903c

One more detail, we also often rent apartments to be able to cook and do laundry. We have used HomeAway/VRBO, Airbnb, and Holiday Lettings.

Have fun planning!

Leave something to come back to. Less is more. Spend 3-5 days Rome, then to Florence (ditto on time) and then get lost in the Tuscan Hill Towns. You will need a car for Tuscany but not Rome or Florence (nor do you want one there).
Here is how I would do it:
Day one: Arrive and settle in Rome
Day 2-5: Rome
Day 6: to Florence
Day 7-9: Florence
Day 10-13: Tuscany
Day 14: Drive to FCO, drop the car off, and fly home.
Enjoy