I just got back from the trip to Italy and wanted to update with the itinerary and some tips that ended up being quite helpful (and differed from what I saw on some forums and travel books).
Cost was around $12000 for 2 individuals, last 2 weeks of September. I loved the Airbnb option, way more spacious and better views than hotels, plus more flexibility.

Day 1
Flew into Rome (O/N flight, arrived early AM), from airport to Airbnb
Spanish Steps and fountain
Church Trinita dei Monti at the top of the steps
Trevi fountain
Church of Santi Vincenzo e Anastasio near the Trevi fountain
Vittorio Emmanuele monument
Trajan's column and forum
Main Roman forum and viewed individual buildings - not listing these all since there are many
SUPER sites: house of Augustus, house of Livia, Santa Maria Antiqua, Imperial Ramp of Domitian, Palatine Museum, Cryptoporticus of Nero, Aula Isiaca and Mattei Loggia, Domus Transitoria, Curia Iulia; Temple of Romulus was closed
Palatine hill and sites there - Domus Augustana, Tiberiana, etc.
Farnese gardens
Basilica of Santa Francesca Romana just by the forum
Tip: Sunday may be a good day to visit SUPER sites as it seems to be one where most/all are open

Day 2
Colosseum main part (separate ticket from arena)
Arch of Constantine
Colosseum arena
St. John Lateran obelisk
St. John Lateran baptistry
Basilica of St. John Lateran
Porta Asinara
Sancta Sanctorum
Basilica of St. Clement
Fontana dei Monti
Arch of Galienus
Basilica of St. Praxedes
Santa Maria Maggiore obelisk
Basilica of Santa Maria Maggiore
Piazza del Popolo
Santa Maria di Montesanto
Neptune fountain
Piazza obelisk
Roma sculptures
Tip: Colosseum is a bit nickle and dime - the best experience is the full experience but tickets sell out online super fast. I chose to get the arena only in addition to regular Colosseum tickets, missed out on the basement and attic.
Tip #2: churches to visit may have closed hours 2-4 or 1-4 or 12-4 or 1-3 or some variety of this. Plan for early afternoon closures and late afternoon or morning visits.
Tip #3: many precious artworks such as the most highly regarded frescoes and mosaics have illumination boxes where you pay 1-2 Euros to light up the mosaics. Well worth it to maximize the quality of pictures being taken
Tip #4: The Sancta Sanctorum is a beautiful site not to miss near St. John Lateran, with amazing mosaic/fresco work but photos are not allowed; the Basilicas of Praxedes and St. Clement also stood out

Day 3
St. Peter's Basilica dome
St. Peter's Basilica main part
Piazza di San Pietro
Church of St. Louis of the French/San Luigi dei francesi
Piazza Navona
Fontana del Moro
Church of our Lady of the Sacred Heart
Church of Sant'sAgnese in Agone
The Pantheon
Basilica of Neptune (back of the Pantheon)
Baths of Agrippa
Basilica of Santa Maria sopra Minerva
Church of St. Ignatius of Loyola
Temple of Hadrian
Column of Marcus Aurelius
Church of San Marcello
Basilica of Sts. Ambrogio and Carlo al Corso
Tip: St. Peter's Basilica dome is well worth the visit
Tip #2: some sites were obscured particularly at the Vatican related to the jubilee (e.g. the baldachin and Pieta of Michelangelo). If flexible, consider postponing Rome vacations to after the jubilee is done to maximize visibility

Day 4
The Vatican Museums and Sistine Chapel
Castel Sant'Angelo
Basilica of Santa Maria in Trastevere
Tip: It is very important to pre-book the Vatican Museum
Tip #2: if the regular site tickets run out you can book a tour - however break off from the tour early since the skip A LOT - they were going to skip all the main Greco-Roman sculpture halls (and Egypt) before I broke off and went on my own (you still have a regular ticket within the tour, so you are entitled to do this)
Tip #3: Vatican museum staff are unpleasant and see this not as an admission to the museum with free walk between halls but a 1-way walkthrough - if you go past a hall you are unlikely to be able to go back to see things, so go slowly through each hall before moving on. I ended up missing the Egyptian hall because the tour skipped it and I broke off only after that - when I tried to reverse directions was shouted at. It's also easy to skip the Etruscan halls unless you go slowly and carefully.
Tip #4: pay special attention to the Sistine Chapel (I preferred the lower frescoes e.g. by Perugino over those of Michelangelo) and the apartments with frescoes by Raphael
Tip #5: Basilica of Santa Maria in Trastevere is well worth seeing

Day 5
Picked up rental car
Pyramid of Cestia
Basilica of St. Paul outside the walls, cloister and museum
Drive to Naples, check in at Airbnb
Tip: it is well worth seeing all 4 major papal basilicas because they are large, ancient, with relics and have very high value art, including usually ancient mosaics and/or frescoes. The 4 papal basilicas should be an absolute minimum set to see in Rome if interested in the church architecture/history.

Day 6
Catacombs of San Gennaro
Piazza San Gesu
Neptune Fountain
Castel Nuovo
Galleria Umberto
Piazza del Plebescito
Royal Palace of Naples (outside) - inside was closed for a political event
Basilica of Francesco (outside ) - square was closed for a political event
Waterfront of Naples
Fontana del Gigante
Castel dell'Ovo (outside) - inside has been closed fro renovations for some time
Villa Communale
Tip: the Catacombs of Naples are well worth seeing

Day 7
Certosa di San Martino near Vomero
Castel Sant'Elmo
Museum and royal forest of Capodimonte
Catacombs of San Gaudioso
Monumental complex of Santa Chiara (part of the catacombs admission)
Gesu Nuovo church
San Domenico Maggiore obelisk
Church of San Domenico Maggiore
Church of San Gregorio Armeno
Church of San Lorenzo Maggiore
The Duomo
The San Gennaro baptistry of the Duomo
Tip: The museum of the chapel of San Severo was booked out and needed prior tickets, so could not see it. I think there may be an important relic there that leads to the high density of visitors.
Tip #2: do not miss the baptistry of the Duomo of Naples

Day 8
Archeological museum of Naples
Drove to Vesuvius/Vesuvio and climbed it
Pompeii archaeological park
Tip: the archeological museum of Naples is a must see, since most the art of Pompeii is housed here
Tip #2: be aware that Pompeii last entry is 2 hrs before closing time - I nearly missed it for this reason - and internally they start closing buildings at 6:20 even if the posted closing time is 7:30, so better to arrive at 4 or earlier to be able to comfortable tour everything
Tip #3: Pre-book tickets for Vesuvius. The last minute thing was a huge pain but basically it is very doable. You do need a wifi connection (they have one on the volcano) and create an account to book the tickets and pay for them. They are released every 10 minutes 30 minutes before the next slot but it's a frenzy with others all trying to book them as well and competing with you for 10 people per 10 minute slot. Early booking online solves this but puts in a time constraint of when you have to visit. Finding the volcano by car was not easy (GPS frequently misdirected) and there can be delays related to this. Once you drive up to a parking lot you will see a shuttle bus that takes you up to the entry site. You cannot pay by cash and there is no place to pay in person by credit card - only online tickets ahead of time or online tickets on your phone while on the volcano.

Day 9
Attempted to visit Tomb of Virgil - closed for renovations
Vista of the Phlegrean fields/Solfatara
Attempted to visit Baiae (closed for the day)
Herculaneum archeological park
Drive to Sorrento area, check in at Airbnb
Tip: Herculaneum's art appears to be mostly on site (unlike Pompeii's) and complementary to and well worth seeing in addition to Pompeii

Day 10
Drive to Positano
Positano cathedral and bell tower
Positano piazza
Positano beach
Drive to Praiano and view of church and square
Drive to Ravello and view of cathedral square
Villa Rufolo
Convent of San Francesco
Villa Cimbrone
Ravello Duomo
Drive to Atrani and view of Umberto square
Church of Collegiata da Santa Maria Maddalena
Tip: part of Villa Cimbrone was blocked off for a wedding - something I imagine can happen at other villas and famous churches. Try to view these earlier in the day since late afternoon seemed to fit more with the villa weddings at least - not sure about churches which may be more of a morning affair
Tip #2: Expensive parking garage in Positano at 10 euros/hr but ample parking if leaving early in the morning, Praiano no problem parking. Atrani has decent parking you can get by driving down to the marina and under the bridge, then up the street and street parking in blue lined spots.
Tip #3: I liked being able to drive around and park and have flexibility and freedom. May not be feasible in June-August peak season but in late September while parking was tight in the late morning/early afternoon, spaces opened up in the late afternoon and early morning and was well worth the money (max 10 euros/hr) over buses/ferries - at least in my view

Day 11
Positano overlook
Furore Fjord
Parked at Atrani (under the bridge) and walked to Amalfi
Amalfi waterfront and Piazza Flavio Gioia
Piazza municipio
Amalfi Duomo, chapel of the Crucifixion
Drive to Vietri sul mar and viewed church of John the Baptist, piazza
Drive to Paestum and view ruins and museum
Tip: for the Furore Fjord, there is no parking there but if you drive past it (in the direction of Salerno) and park at the Ristorante Euroconca they offer parking if you buy some food/drinks at their place - it came to 10 euros for 1 hr, which was worth it
Tip #2: Paestum is a delightfully quiet place compared to the Amalfi coast and was a nice conclusion to the business of the Amalfi coast earlier that day

Day 12
Took NGL-Gescab ferry from Sorrento to Capri in AM, arrived to the Sorrento marina around 9:50 or so and got to Capri at about 12 PM
Marina Grande
Piazzetta di Capri
Piazza Umberto
Clock tower
Gardens of Augustus
Lookout points onto Faraglioni
Certosa San Giacomo
Villa Lysis
Walked back to Capri and took bus to Anacapri
Church of San Michele
Church of Santa Sofia
Taxi back to Marina grande
Ferry back to Sorrento
Sorrento marina
Sorrento church of San Francesco
Tip: either pre-book Capri NGL-Gescab tickets and stick to the schedule or anticipate the last 1-2 ferries back may be booked out. We were planning on buying day of to have flexibility and not knowing how much there might be to see on Capri but got stuck with 5:45 PM tickets rather than the intended 7 PM tickets.
Tip #2: Blue Grotto tour is a boat to the site, then a rowboat apparently into the Grotto - did not take this tour but in retrospect would have liked to have had time for the regular boat tour around the island
Tip #3: the funicular can be extremely busy as can the buses - we ended up walking from the marina to the main town of Capri to save time
Tip #4: worth viewing the San Michele church in Anacapri, which has unique large Majolica tile flooring
Tip #5: the buses get awfully slow/sparse around 5 PM from Anacapri - which I suspect is by intention - so if you have a ferry to catch get ready sooner or you may need to take a taxi to make it, as we did.

Day 13
Sorrento Piazza Tasso
Basilica of St. Anthony
Duomo
Dominova Seat
Drive to Rome
Attempted to view catacombs, closing/closed
Rome check in at hotel
Tip: do not overlook Sorrento, I preferred it much over Amalfi coast towns, although it is less popular.
Tip #2: the Roman catacombs have odd hours (9:30-12 and closed 12-2, then open 2-5 but last entry before 4:30, etc.) - please be aware of these restricted time windows in your planning

Day 14
Church of Santa Maria dei Miracoli
Basilica San Giacomo
Church of Santa Maria in Via
Basilica of the Twelve Apostles
Basilica of Cosmas and Damian
Basilica of Santa Maria in Aracoeli
Capitoline Egyptian Lions
Capitoline Hill
Theater of Marcellus
Portico of Octavia
Great Synagogue (outside) - inside closed given it was Saturday
Temple of Janus
Basilica of San Nicola in Carcere
Temple of Portinus (outside)
Santa Maria Cosmedin and crypt
Mouth of Truth
Basilica of Santa Sabina all'Aventino
Belvedere Luigi Magni
Circus Maximus
Baths of Caracalla
Gardens of the Villa Borghese
Galleria Borghese
Tip: two hours is plenty of time to see the Galleria Borghese and a late time ticket was a nice way to cap off the day. Book well in advance as these sell out quick
Tip #2: the Baths of Caracalla and the Basilicas of Cosmas and Damian and Santa Maria in Aracoeli as well as the Santa Maria Cosmedin church all stood out and are well worth visiting

Day 15
Fly out of Rome


Restaurants and pastry shops/cafes that stood out: Bareto in Rome (cafe near the Spanish steps), Dilla in Rome (restaurant near the Spanish steps), Fraschetteria Giampiccolo in Rome (restaurant near the Villa Borghese); Sorbillo in Naples (pizza chain, tried the flagship one), Poppella's in Naples (dessert chain), Pompi in Rome (dessert chain); Trattoria San Gennaro in Praiano (the single best restaurant I tried in all of Italy, get the lemon sorbet and delizia)



Overall I was very happy with the trip variety, food, planning. More advanced planning would have enabled seeing a few more things. The tempo was fast and physically exhausting but not mentally saturating. Big takeaways were that Rome has an abundance of amazing historic churches and monuments from the Roman Empire to see and you could spend another 1-2 weeks trying to see the rest of them, Amalfi coast is very doable by car in late September, be aware of nonstandard hours (for American tourists) with potentially large breaks in the midday that would prevent you from touring sites (especially churches) - so plan accordingly.

More things? Even with a scooter I've no idea how you crammed in what you did.

Man, where are you going for a holiday? ;-)

Wow, I can see why it was exhausting! Did you just check things off a list? You certainly didn't have time to really see and experience all these places. Actually, I don't see how it was physically possible to do all this! I'm just curious, when did you find time to eat?
Well, this definitely proves different strokes for different folks.
Glad you enjoyed it!

Haha, my vacations are more like expeditions to try to see and experience as much as possible from sunup to sundown, so I do need to recover when I’m back. I walked an overage of 9 miles a day and got some golfers legs/exercise induced vasculitis but that’s resolved.

I did have time to see things and reflect on them. I woke up at 4-5 am most days and filled things with activities until sunset. I planned the most efficient walk itinerary I could the night before or morning of, walked quickly, read posted signs on interesting parts of things (I did not photograph every chapel of every church or read about the artist if I thought it was not particularly good). I did study mosaics and frescoes in detail and also relics. In museums I inspected all galleries and most pieces and photographed many. Skipped lunch and snacked instead most days (eg eating a pastry or fried seafood while walking instead of sitting down to a formal lunch) but always had nice dinners, usually at 7:30 or later.

You should take a look at my 2 week Turkey itinerary, lol.

It was enjoyable all around. Would probably need another six 2-week blocks to take in the rest of Italy. But anticipate the next few vacations will be the UK, Greece, and Egypt, possibly India or Turkey.