Sorrento, sitting on the south shore of the Bay of Naples is about an hour's drive from that city and makes a very good center of operations for a three or four day stop in this area. Amalfi is to the south, Pompeii to the east, and the Isle of Capri just to the west in the Bay.
So we start by taking a short ferry ride to Capri, a four by two mile island that has became a tourist zoo in July and August, it's a tourist trap, plain and simple, during the height of summer. Early spring and again in late September the Island becomes enjoyable again. It originally became famous as the vacation home of the Emperors Augustus and Tiberius. There are a few Roman ruins about (name me a spot around here that doesn't have Roman ruins!), and an eight hundred year old monastery inhabited by Carthusian monks, its chief attraction is its Blue Grotto.
The Blue Grotto - I hate to keep saying this because I know these people have to make a living - is a TOURIST trap big time. There are three ways to get there: by boat from the harbor, by bus up the road to Anacapri, and hiking up the Phoenician steps, all 800 of them! The bus is the best bet, and certainly a lot cheaper than going by boat. The bus stops quite a distance above the water, you descend the steps hewn into the rock down to where you pay. Did I say pay; you pay three times, once for the boat to the Grotto, again for the rowboat into the Grotto, and again for the entry fee. From mid June to mid September there's usually a lineup for your turn in a rowboat. Twenty minutes, a half-hour tops to rowboat, visit, and return to your boat.
You need the rowboat because when you get up to the entrance, you have to get down on the floor of the boat, the oarsman grabs a chain along the wall and pulls the boat in. And, yes, it really is blue. If you're on Capri or even in Sorrento, be sure to go. Just make up your mind to go with the flow, put up with the touristy stuff; and see the Grotto. ONCE, I would never go back.
Second day is a trip east to Pompeii. This is where Mount Vesuvius erupted in AD 79, and as you explore the excavated ruins, you get a first hand look at what life was like in Roman times. It had a population of 20,000 when it was buried under thirty feet of hot mud and volcanic ash, but its best art has been removed to the Naples Archaeological Museum. It was a bustling city, with so much traffic that chariots were banned during shopping hours. You see the odd street sign picturing men carrying vases, apparently this meant "Pedestrians Only".
Herculaneum, much smaller, less ruined than Pompeii, it has a small number of intact surviving buildings.
And then there's Mount Vesuvius itself. Some 4,000 feet high. If you have a car you can drive up to the summit, there's a kind of shuttle bus that trundles up and down all day, or if you're in the chips take a taxi, but get a quote from several before choosing one. There's a sort of trail you can follow if you want to hike around the rim. Vesuvius has been rumbling and shooting off steam since 1944, but is not considered really dangerous any more.
Third day is the highlight of this mini tour, the Amalfi Coast. For the money, the road from Sorrento through the towns of Positano and Amalfi to Salerno is one of the best bus rides in the world, and is not for the weak at heart. There are sheer drops of 4 to 500 feet off the side of the road down to the shoreline below. Grab a seat on the right side of the bus from Sorrento, and then a seat on the left for the ride back after a few stiff ones in Salerno for fortification of the spirit. There isn't a level piece of land anywhere, yet both sides - up the hillside and down towards the water - there are hundreds of dwellings, hotels, villas and garages. Traffic along this road is so heavy in the summer that cars with even numbered licenses are allowed to drive one day, odd numbered the next. Buses and tourists who hunger for the ultimate thrill drive any day.
Enjoy the ride along the road, you probably won't enjoy the towns along the way. Over-crowded, over-priced and out of reach for the most part of the beaches far below. Positano is the best bet if you want a stopover here. It's on a short stretch of pebbly beach and has the obligatory expensive collection of women's clothing stores and caf