Where in Italy to go with kids for a first timer?

[Ihaveattached]

Grateful for any advice. We've never been to Italy, but have always wanted to go.
It would be end of August next year as we are bound by school holidays. We already have a holiday booked for May half term, wont have saved up by Easter and have heard October won't be warm enough for the pool.

We have a 13yr old who loves history, food, swimming and a 6yr old who has no interest in Italy but would love swimming in the sea or a pool.

We definitely don't want to do any driving but are happy to have trips out by boat or train.

We thought of Sorrento as you can easily have trips out to Capri etc. We'd need a bed and breakfast and don't want anywhere chintzy. I know it doesn't seem important but I can't settle if I hate the decor in a hotel so the more modern the better.

We like having somewhere to have a stroll on an evening. I heard Naples is a really busy city so I'm not sure our youngest would cope with that as he has sensory issues.

We don't just want a sunbathing holiday. We want to see a bit of Italy.

Any ideas?

[AdriannaP]

@Ihaveattached sounds great! Have a lovely holiday