The south is a different country
Everything north of Rome runs on timetables. Everything south of it runs on nerve, and that is exactly why we loved it. This route strings together Naples, Pompeii, the Amalfi Coast and the cave city of Matera in ten to twelve days, using the scrappy local trains and buses that keep costs at a fraction of what the coast's reputation suggests.
Naples, three nights
Naples gets slandered constantly and deserves none of it. It is loud, gorgeous, and serves the best pizza on earth for 5 to 7 euro a whole margherita; the famous places have queues, but the unfamous places two streets away are nearly as good and empty. Walk Spaccanapoli end to end, go underground into the Napoli Sotterranea tunnels (about 15 euro), and give a full morning to the Archaeological Museum, because everything beautiful that was dug out of Pompeii lives here, not at the site itself. Dorms run 25 to 40 euro, the cheapest on this whole route.
Pompeii and the Circumvesuviana
The Circumvesuviana is a battered commuter train that leaves from Napoli Garibaldi and costs about 3.50 euro to Pompei Scavi. It is graffitied, crowded and completely safe; just keep your bag in front of you. Pompeii itself costs 18 euro and needs five hours minimum. Go at opening, walk straight to the far end at the Villa of the Mysteries while everyone else clusters at the entrance, and work your way back against the flow. In summer there is no shade at all: hat, two litres of water, no exceptions.
Sorrento to Positano to Amalfi
Stay the night in Sorrento (dorms 30 to 45 euro), then take the SITA bus toward Positano, about 3 euro, sitting on the right side for the drop. Fair warning: in peak season the bus queue is grim, so we did the smarter thing on the return and used ferries. Positano to Amalfi by boat costs 10 to 15 euro, takes 25 minutes, and gives you the postcard view of Positano stacked up the cliff that you simply cannot get from inside it. Positano is a look-around town for a backpacker, not a sleep-in town; base yourself in Amalfi or, better, take the tiny local bus up to Ravello, where the Villa Cimbrone terrace hangs a thousand feet over the sea and costs 10 euro to enter. The Path of the Gods walk from Bomerano down to Nocelle is free, takes three hours, and was the best half day of our trip; start by 8 am before the heat and the tour groups.
Salerno, the honest base
Here is the money-saving secret of the Amalfi Coast: sleep in Salerno. It is a normal, likeable working city at the coast's eastern end, with ferries and buses running the whole coastline, real restaurants at real prices, and beds at half the Amalfi rate. The evening passeggiata along its seafront is as Italian as anything on the fancy side of the cliffs.
Matera, the detour that steals the show
From Salerno, buses run inland to Matera in about two and a half hours (12 to 18 euro, book a day ahead). The Sassi cave districts, inhabited for nine thousand years, emptied by decree in the 1950s and now slowly reborn, are unlike anywhere else in Europe. Walk down into the ravine on the far side at sunset and watch the whole stone city turn the colour of honey. Two nights is right; cave-room guesthouses start around 40 euro a double, less than a Positano dorm.
When to go and what it costs
May, June, September, early October. August is genuinely difficult: full buses, full ferries, forty-degree stone. We averaged 65 to 80 euro a day each in shoulder season, and the biggest single saving was sleeping in Naples and Salerno rather than on the coast itself.