If you choose one ancient nuraghe to visit, make it Su Nuraxi. It gives you the best sense of the primitive grandeur of Sardinia's only indigenous Bronze Age civilisation. A UNESCO World Heritage Site, it's the largest and probably the oldest nuraghic complex on the island, dating from around 1500 BC.
The central tower once reached 21 metres (now under 15m after partial collapse) and is surrounded by four smaller towers and the remains of a substantial village of circular huts. It was almost certainly a palace complex and possibly a capital city. The whole structure is thought to have been buried by Sardinians and Carthaginians at the time of the Roman conquest — which accounts for its remarkable state of preservation. It was only fully excavated in the 1950s.
Guided tours (the only way to visit the interior) run throughout the day. An Italian-speaking guide is always available; English-language tours run less frequently, so check timings when you arrive. The site is open daily from 9am to an hour before sunset.
Su Nuraxi is located a kilometre outside the village of Barumini, 50 km north of Cagliari. By public transport, there are two daily ARST buses from Cagliari that stop here en route to Désulo and Samugheo; by car it's straightforward via the SS131. In the village, the Casa Zapata museum has finds from the excavation and — remarkably — preserves a nuraghe beneath its own glass floor.