We had our honeymoon in Sorrento, first 2 weeks of October. A couple of decades ago now but I remember it was gorgeous weather. Herculaneum, Pompeii, Vesuvius, Positano. All beautiful and all done by train rather than organised trips. Amalfi coastline is beautiful too. And easy to walk to the harbour and get boats to Ishcia and Capri. Ischia is less well known than Capri and much quieter (well, it was in the 90s!). We spent alternate days on day trips exploring and the rest lazying by the hotel pool and pottering around Sorrento, it was the perfect balance for us.
You'll have an amazing time, it's a beautiful part of Italy. And Sorrento centre is lovely, lots of cafes, ice cream, pizza. Great for people watching (and trying not to be killed by crazy moped drivers!) Actually, that reminds me, it rained a little a couple of times, we laughed that the moped drivers used one hand to steer and the other to hold an umbrella up.. all in a sleek Italian suit 😆.
It was just before the millennium when we went and Rome was covered in scaffolding, having a face-lift for the 21st century; otherwise we may have done a dual site holiday and stayed there for a few days too, it's not far.
Back in the day we were told to avoid Naples. As you got nearer on the train to Herculaneum , the graffiti and litter increased in the stations. I would avoid Naples.