Although things may be less crowded in October, you should check online climate sites for water and air temperatures. You may also find that a few coastal businesses close for the season around then. Are you aware that Sorrento is not a "beach town?" It's built on a sheer cliff.
You have not filled out your "home area" in your visible profile, so we have little to go on when you describe fear of Naples. Street crime is much lower in Europe than in the US, and Naples' problems are about limited government and infrastructure funding, not rampant crime. It is unlike northern European cities, but it is loaded with art and history. You need to study it further to see if you want to spend a few days there, or go to an island or the actual Amalfi Coast. Naples is pretty easy to get to from Sorrento, just over an hour on the gritty commuter train, the Circumvesuviana.
Have you used the Search box here to explore getting to Sorrento from Rome? It's just over ONE HOUR on the slightly more expensive Frecciarossa train service to Naples, and then another hour on the Circumvesuviana or in a private car or taxi. Do you really "need" a stop along the way? Rome is good for a full week for most people.
Two special places I could name are "too close" to the ends of your journey, Tivoli and Caserta. (Have not made it to Caserta yet.) There are lots of people on this board who like Salerno, but I haven't been there. It has good access to Pompeii and Paestum. The latter is hard to get to from Sorrento, but we don't know if it would interest you.
Your screen name suggest you might be one of the UK people whose first question on Trip Advisor is, " 'ow much is a Pint in Sorrento?" (smiley face)
