Naples/Capri, Salerno/Amalfi Coast, or Pompei - 1 night/2 days to spend

My vote is always for the AC. That being said, it really depends on the time of year. When is this trip planned and have you been to any of these places before?

Do you really have two full days extra?
If Naples, do you really have time for Capri too?
You could do an overnight to Capri.

I've spent a less than a day in Naples, and have never been to Capri. BUT...

In April, we spent several days in Salerno, and highly recommend it - don't miss the tomb of the Apostle Matthew in the Duomo. On one day, we hired the owner of our B&B to drive us to Ravello - where we explored Villa Cimbrone on our own. Later, he drove us to the dock in Amalfi, where we had chartered a boat for a ride along the coast from Amalfi to Positano, and then back to the dock in Salerno. I would highly recommend this experience.

https://www.blumediterraneosas.com/

https://www.salernocentro.it/en/

https://www.hotelvillacimbrone.com/villa-cimbrone/

But if you really want a glimpse of Ancient Rome, then spending a night in Pompei to tour the ruins could be equally amazing. Our hotel and guides were exceptional.

https://hotelforumpompeii.com/en/

https://www.askostours.com/

I don’t know how you get 2 extra days and only 1 night. By train, it takes about 6 hours to get from Tropea to Rome and 4 hours from Tropea to Salerno which is on the T to R route. I’ve not stayed in Salerno but used it as a way point where I picked up a rental car before heading East & South into Puglia after Amalfi. We used ferries along the Amalfi coast from Naples to Capri to Sorento to Amalfi (then Positano to Amalfi) and finally to Salerno. A day ferry trip from Salerno could get you to any town along the Amalfi coast or to Capri and back to Salerno to catch a late (or early) train to Rome. You could take a trip from Salerno to Paestum for more Roman ruins or catch it on the way from Tropea. So many options.

Thanks, everyone, for the input! Timing - end of Sept 2022, we have a 1 night/2 days because we're checking out of Tropea on a Monday morning and not flying out of Rome until Thursday morning. We could stop over in Naples/Capri, etc. on Monday night at the least and possibly Tues as well if we really wanted. I've got friends who are suggesting Positano and a day excursion to Capri.

Thanks, everyone, for the input! Timing - end of Sept 2022, we have a
1 night/2 days because we're checking out of Tropea on a Monday
morning and not flying out of Rome until Thursday morning. We could
stop over in Naples/Capri, etc. on Monday night at the least and
possibly Tues as well if we really wanted. I've got friends who are
suggesting Positano and a day excursion to Capri

I read this as 2 nights to spend. You need to be in Rome Wednesday night.

Do you have reason to be in Rome on Tuesday night/Wednesday? If you have spent time there already and just need to return to fly home, I’d use the 2 nights you have elsewhere. But I’d caution you to not overplan even that short amount of time. Getting to Positano takes time (it was worth a few hours to us), as does getting to Naples and Capri.
Naples deserves more than a half day and so does Capri. Save for next trip.
Your first day is more than half gone just getting north from Tropea.

Are you driving or taking train from Tropea?

We enjoyed our 2 nights in Salerno very much. (after a week in Sorrento/Amalfi)
Direct train to Rome from Salerno. Good eats, cheaper lodgings, fun passeggiata, nice historic center, lungomare with views of Amalfi Coast and non-touristy.
You could visit Paestum or Pompeii or Amalfi/Ravello quite easily. Only you can decide which is priority.
Salerno is on the way to Rome, easy to get to, train/ferry right there. You have 1.5 days. Don’t overplan and spend any more time in transit than necessary.

Christine wrote exactly what I would have, except that she writes better than I do.

Month of the year?

Capri takes a full day, from a town with a ferry. It's not a part-day excursion, and has a lot of pedestrian-only walking and sun exposure. Pompeii is also hard work, but can be a half day from Sorrento or Naples, not from Positano unless you hire an expensive car service. Can go to Pompeii from Salerno by rail with taxi in modern Pompeii city.

For a single night it makes more sense to use Naples or Sorrento for good transit. You may be underestimating travel effort on the actual Amalfi coast, and to Tropea. I have not been to Salerno, but it is simply not as popular, except as a base for Paestum. Note that the Salerno ferry to Capri takes longer. You need a backup in case the water conditions cancel a ferry, not common though.

Right, we've assuming you're traveling by train, and not in the off season?

Off top of my head, I'd say Naples with a day trip to Capri if the weather cooperates and if you're going in a warmer month. While Naples is a high-energy place, it offers ferry service to Capri, some quality sightseeing in the city itself (Recommended: the National Archeological Museum where treasures from Pompeii and Herculaneum reside; closed Tuesdays), and, of course, Pompeii and Herculaneum are just short trips away by local commuter train.

Shortest journey time by rail from Tropea to Napoli Centrale is abt. 4.5 hours and one train change. Getting to Positano is sort of a pain so I'd save it for a future trip when you can give the region the time it deserves.

we're checking out of Tropea on a Monday morning and not flying out of
Rome until Thursday morning.

So you could be in Naples by very early afternoon, giving you 1/2 day or so to explore (that's when I'd do the museum) then the entire day Tuesday (Pompeii and more Naples exploring) and Wed. AM before you leave for Rome.

Museum website:
https://mann-napoli.it/en/home-english/
https://mann-napoli.it/en/timetables-and-fares/

Alternately, you could train to Naples, get a cab to the ferry port and head to Capri. Stay Monday and Tuesday nights there, and head back to Naples and on to Rome on Wed. Ferries run to Capri from Naples all year except in the most unsafe sea conditions.

It’s much easier to reach the Amalfi Coast from Salerno. Service is good by both ferry and bus.

https://www.travelmar.it/_download/orari-travelmar-luglio-2022.jpg

https://www.sorrentoinsider.com/en/sorrento-to-positano-bus-schedule?route=amalfi_maiori_salerno

If you’re leaving Tropea on Monday in the a.m., you should be in Salerno by 13-14:00. Time to check into your lodging and have a leisurely walk around the Medieval city.

Tuesday, you could take the ferry to Amalfi 35 minutes or continue on to Positano an additional 40m. This would be w/a change of Ferries in Amalfi. ( I’m another not enthralled by Positano).

There are many other towns on the southern end of the coast Ravello, Atrani, Minori Cetara, Maiore and Vietri sul mare. Use the bus to connect these on your way back to Salerno.

Wednesday, you could visit Pompeii. Take your luggage with you. Train to the city of Pompei, 1H11m then a 5m taxi ride to the Scavi site. Check your luggage at the entrance. Guides are available at the site. Suggest 3-4 hours.

To reach Naples use the Circumvesuvian train, to Napoli. Here you can book mid-late afternoon train to Rome 1H17m.

Edit.

https://www.visitpompeiivesuvius.com/en/naples-to-sorrento-train-schedule?route=sorrento_napoli