While not strictly accurate I'll use Amalfi Coast to cover Amalfi, Positano, Ravello, Capri, Sorrento, Pompeii and Hurculaneum, all of which are wonderfully picturesque and fit nicely into the stereotypical Italy. Except for nearby Naples - once glamorous, now dirty, seedy and controlled by the Mafia, who quite obviously have not mastered the niceties of the tourism business. Apart from its hosting of the train terminal there is no reason to go there. Vesuvius would do Italy a favour if it blew again and buried the place - provided it spared next-door Hurculaneum which it covered in volcanic mud the first time and which is well worth an explore, being in even better condition than Pompeii which was smothered in ash rather than mud, the weight of which collapsed its buildings.
Sorrento is an ideal base from which to visit the other locations. It's central, it's large enough to cope with the milling throngs of tourists that can overwhelm the smaller towns like Positano and Amalfi and it has plentiful classy amenities, amongst which is the Hotel Minerva high on the headland with spectacualr views across the Bay of Naples to Naples itself which is far enough away to just look like pretty lights, and to Pompeii and Mt Vesuvius. The terraced hotel has large, sea-facing open areas, with our rooms having dedicated partitioned balconies on which to relax and take in the view. Highly recommended by The Ruins.
Sorrento is an easy half-hour stroll from the Hotel. Capri, Amalfi and Positano are readily accessible by boat with the rugged coast making the trip worthwhile on its own. A road alternative by Ducati or Ferrari would be a treat - the windy road high up the mountain side would be a riders/drivers heaven. We jumped aboard a smallish motor launch at the Marina della lobra, a short bus ride away.
Positano, Amalfi and Ravello are lovely but the tourist multitudes can make them horrendously claustrophobic. Regular buses from Amalfi make it easy to visit Ravello high up on the mountain via multiple hairpin bends and you'd be nuts not to head up, take in the scenery and have a poke around - it's a nice little village with a main piazza, galleries and cafes sans the milling hordes who must find the slight extra effort to get there as too much just for a gelato and a selfie.
Sounds glamorous. A bit swish in parts with expensive looking villas on the switchbacked road up from the pier and ritzy Italian fashion outlets. But it accommodates us riff-raff with an easy open-top cab ride via a narrow road that in places hangs out from the cliff face and chair lift to the highest point that offers superb views as a supplement to the sticky beaking into backyards and laundries from the chairlift. The leather clad, patch-wearing, hairy and tatooed bikers (that was just the women) trying their best to look cool on their descent didn't quite carry it off. It's not easy to look scary when the average age of your gang is about 70 and your Harley is to be traded in on a mobility scooter in the near future.
Both places were victims of Vesuvius's eruption in 79AD, with Hurculaneum being buried in volcanic mud flows while Pompeii was covered in falling ash and debri which collapsed most of its buildings. The victims in Pompeii are well known from the casts made of their bodies from the cavities they left in the fallout. The victims' remains in Hurculaneum are skeletons, uncovered in arched boat-houses in what was then the waterfront.