Three days between the sea and two thousand metres
From the pine woods of Metaponto to the Pollino and back, with a night in Matera in between.
This tour works by keeping a base on the Ionian coast and moving out like spokes on a wheel, which is how Basilicata lets itself be visited best: the open-air sites are almost all there, and everything else in the region is within two hours' drive. If you only have a weekend, do days one and two; if you have a week, add Maratea, which is on the other side and calls for a proper move.
Day one: Magna Graecia and the pine woods

The first day stays on the coast and serves to get your bearings. From a base between Metaponto and Policoro the Tavole Palatine are a quarter of an hour away: fifteen columns of a temple to Hera, standing in the middle of the countryside, without scenic fencing around them and without a monumental ticket office. It is one of those places where antiquity is easiest to see precisely because nobody has staged it.
In the afternoon, the Museo Archeologico Nazionale della Siritide at Policoro, with the grave goods of Herakleia, and then the Bosco Pantano: what is left of the lowland forest that covered the whole Ionian shore before the land was drained. On the beach in front of it, in summer, sea turtles lay their eggs, and the nests are marked and fenced: you look from outside.
Day two: Matera
On the second day you go up to Matera, a little under an hour. It is worth arriving early and leaving the car in the car parks outside the Sassi: inside you walk, and the gradients are serious. Give the morning to the Sasso Barisano and the Civita, with the cathedral on the spur; give the early afternoon, when the sun is hard, to the things underground, the palombaro lungo cistern and the rock churches.
Towards evening, cross to the other side of the Gravina, onto the Murgia plateau: from there you see the whole city, from bottom to top, and that is the point from which you understand how it is built. If you feel like walking you can go down into the gorge and climb back up; if you do not, it is twenty minutes by car.
Day three: the Pollino

The third day is the longest. You head west towards the Pollino, a good two hours of ridge roads, entering from the Basilicata side through Rotonda, Viggianello or Terranova di Pollino. The massif rises above two thousand two hundred metres and the paths start from the mountain huts and the high plains: even an hour's walk brings you within sight of the Bosnian pines, which grow clinging to bare rock and have bark split into plates, like armour.
This is real mountain country, not high hills: in summer the storms arrive in the afternoon and the mist comes up fast. Boots, water, a jacket, and a look at the forecast before you set off. If you would rather not climb, you can stay low and walk the Raganello gorges in summer with guides, wading up the stream.
The fourth day, if there is one
With one more day, spend it in the Lucanian Dolomites, between Castelmezzano and Pietrapertosa: two villages wedged into sandstone spires, half an hour of hairpins apart, linked by a steel cable you fly along in a harness. With two more, cross the region to Maratea and take a day of an entirely different sea: cliffs, coves and water that drops away at once.