Coastal trip including naples

so my family and I are going to Italy for 2 weeks from September 1st to 14th, we are starting in Naples and spending around 4-5 days there. and after that we haven't really got a proper idea of where to go. I got my family to all tell me the things they wanted from a holiday I'll post the list below apologies because it's probably a bit incoherent. I really love the historical side to Italy but my family tends to get bored of that fairly quickly which is a bit of a shame but I'm hoping that we can find a mix of everything to make everyone happy and I would really appreciate any ideas!

the places I've looked at other than Naples are tropea, Sorrento, Salerno, Puglia, palinuro, Bari and terracina

this is the list, apologies again for it being a bit messy and thankyou so much in advance for any idea or help you could give:

- beach

- history

- mix of culture

- affluent and mature

liked hvar (but would have liked more to do)

- Walking along the beachfront

- not a tourist trap

- a proper purpose not just a way to spend a day

- somewhere tropical

- near a waterpark or

Enough to do for 4 days

Has a charming old town but not staying in the charming old town

Roman ruins but not the main focus

lots to do and see (and eat)

Lots of shops restaurants bars and gelato

Not crazy overpriced but it doesn't have to be budget

volcano views (but I guess we'll probably get those in Naples)

On the coast not the islands

Near a marina or a beach promenade

An old town within walking distance

Cute little markets for gifts and souvenirs

Street food areas