I know the campania region really well (Naples/amalfi coast) having visited various places over many repeated visits… even got married there! I’m going again tomorrow, so can answer any specific questions you might have.
Yes Sorrento is convenient public transport wise if coming from Naples, but I disagree it’s a good place to stay to access the Amalfi Coast , it’s actually not on the coast and travel by bus is slow. Taxi too expensive. But boat is better.
Sorrento is in a lovely setting but it’s not a very interesting place to stay. The food caters more to British tourists than Italians, and it shows in quality/taste. There’s not much to see/do. But it is a great place to visit Capri as ferries are regular. There are no beaches in Sorrento. It’s possible to enter the sea using “beach” clubs (strips of concrete) which are the least appealing places to swim along the whole coast.
Maiori, Minori and even Salerno (and all in between) are far better places to stay on the Amalfi Coast as they’re family friendly and much cheaper. Really easy to reach the classic destinations (Amalfi, Positano) by bus (or ferry in summer). Positano is nice to visit for a day trip but I wouldn’t recommend staying there - would be spendy! I love these southern towns/villages because they’re popular with Italians so the food is great and good value. They also have a better family vibe. They are also really easy to reach now with the newly opened Salerno airport which EasyJet flies to. Saves going to Naples.
Personally I don’t like Capri because it’s so small and crowded it’s really not pleasant. I’ve tried many times and it’s always the same experience . If you’ve been to Florence it’s a similar level of crazy crowds. Stunning scenery but you feel like cattle being herded along.
Far, far nicer is Ischia island which is AMAZING! So much to see and do there, teens would love it. There are spas galore dotted around the island. You can do a day trip from Naples but better to stay for 3/4 days. It’s not as easily accessible from the Amalfi coast as Naples. Again it’s popular with Italians and Germans. It’s popular but much bigger than Capri and more chilled. Prices are super competitive- I’m always getting sent cheap AI deals from hotels I’ve stayed in. The hotels have decent food not like your normal AI package holidays. It’s not somewhere I’d recommend driving but the buses and ferries make travel easy and a lot of hotels provide free shuttles to beaches and towns. Very family oriented place. Reach from Naples on ferry.
Naples itself is a brilliant city to visit with teens. It’s edgy and loads of history. So much to see and explore including the underground tunnels/caves which they’d enjoy. Then there’s the pizza, street food. History and archaeological museum (which is always very quiet). I’ve taken kids here and it’s been fine (stick to the main drags when walking and taxis for further distances I’ve never felt unsafe).