A Wiki article on
nuraghi discusses the etymology along with dating and function. First up is our own inestimable OED:
"
The word is perhaps related to the Sardinian place names Nurra, Nurri, Nurru, and to Sardinian nurra 'heap of stones, cavity in earth' (although these senses are difficult to reconcile). A connection with the Semitic base of Arabic nūr 'light, fire, etc.' is now generally rejected."
followed by
"
An etymological theory suggests a palaeo-Basque origin by the term *nur (stone) with the common -ak plural ending;[5] the Paleo-Sardinian suffix -ake it's also found in some indoeuropean languages such as latin and greek.[6] Another possible explanation is that the word Nuraghe came from the name of the mythological hero Norax, in this case the root *nur would be an adaptation of the indo-european root *nor."
Just across the way to the north of Sardinia is Corsica, once colonised by Phoenicians/Carthaginians, which has similar structures known as
torri, plural of torre i.e. tower.
The reference to Norax seems to be an 'explanation' of the Nora Stone "still considered the oldest Phoenician inscription yet found in Sardinia and the oldest inscription in the western Mediterranean"....dated rather conveniently to coincide exactly with the supposed age of the nuraghi, i.e. probably ninth-century BC.

The town of Nora was built in the south on a peninsula by the Phoenicians, whether or not nuraghi were already in situ isn't known but it is believed to be the oldest town in Sardinia.
According to legend, Nora was founded by a group of Iberians from Tartessus led by Norax, a mythological hero son of Eriteide and the god Hermes.[2] It is believed to be the first town founded in Sardinia and to have been settled by the ancient Sherden or the Nuraghi people, and later colonized by Phoenicians.
"Sherden" is one of several names that vaguely refer to 'Sea Peoples'. Even less is known about 'Nuraghi'.