My ventures to that area have revolved around ruins.
Herculaneum is more compact and easier to "do" than pompei, but I prefer pompeii. I wouldn't do both in one day.
Also on the circumvesuviana (the suburban railway that takes you to pompei) at Torre Annunziata is a fabulous hidden archaeological gem, Oplontis Villla Di Poppea. Highly, highly recommend and it's less tourist than pompeii/herculaneum.
Herculaneum and Villa Di Poppea would be a nice full day. Pompeii one day of its own.
If you're going to Pompeii I'd get the Trenitalia service from Napoli Centrale to Pompei rather than the circumvesuviana, then go through the modern town which is lovely and has a lovely church at the centre. It's a short and pleasant stroll to the ruins, and there are lovely less touristy restaurants and cafes on the way.
Capri is nice but alarmingly expensive, I wouldn't say it's a must do. If you do go, walk up to Villa Jovis (ruins of the home of Tiberius). Sit down before you order an ice cream to save you from falling over when you get the bill 😆
Sorrento I'd not bother with on a short trip, it's basically tourist central.
A fabulous and little known place to go is the temples at Paestum - simply stunning. Good little museum and a lovely local area.
Vesuvius is a great trip too - get on the Public Bus of Terror for added flavour to your holiday! You'll be planning your funeral as you are flung round the mountain road bends 😂
In Naples itself we love the Zoo Di Napoli. it's been beautifully and lovingly restored over recent years. We've visited from its darkest days when it reopened around 2015, it's a lovely place now and well worth a visit.
I'd be interested to know if the lifts at Naples station have been fixed, they appear to have been out of order for about 15 years 😂