‘…we came to the lofty citadel of Lamus, even to Telepylus of the Laestrygonians, where herdsman calls to herdsman as he drives in his flock, and the other answers as he drives his forth.’  Odyssey 10.81ff. (online text: Eng., Grk.)
[here and below quotes are selective; follow links for complete passages]

Ancient Localization

Hesiodic Catalogue of Women,  fr. 150.26 M-W

[The Boreads chase the Harpies] “about the steep Fawn mountain and rugged Etna to the isle Ortygia and the people sprung from Laestrygon who was the son of wide-reigning Poseidon.”
(online text: Eng. [fr. 40a at this site])

 

Thucydides, History of the Peloponnesian War 6.2.1

“It (Sicily) was inhabited in old time thus, and these were the nations that held it: The most ancient inhabitants in a part thereof are said to have been the Cyclopes and Laestrigones, of whose stock and whence they came or to what place they removed I have nothing to say.”
(online text: Eng.Grk.)

Apollonius of Rhodes, Argonautica 4.964ff.

“…the heroes caught the wind and sped onward; and swiftly they passed the mead of Thrinacia, where the kine of Helios fed.”
(online text: Eng., Grk.)

Crates of Mallus, fr. 50 Broggiato

Crates of Mallus thought the Laistrygonians lived in the north, based on the Homeric reference to long days in Telepylus.

Horace, Ode 3.16.34ff.,  3.17.1ff.

3.16: “Though it’s true the Calabrian bees don’t bring me/their honey, and no Laestrygonian wine-jar/mellows for me…”
[Latin: nec Laestrygonia Bacchus in amphora / languescit mihi ] (online text: Eng.Lat.)

3.17: “Aelius, of Lamus’ ancient name…./No doubt you trace your line from him,/Who stretch’d his sway o’er Formiae”
(online text: Eng., Lat.)

Cicero, Letters to Atticus 2.13.2

“When you come to “Laestrygonia of the distant gates” — I mean Formiae— what loud murmurs! what angry souls! what unpopularity for our friend Magnus!”
(online text: Eng.Lat.)

Ovid, Metamorphoses 14.233-234, Fasti 4.69

Met.: (Macareus, surviving companion of Odyssseus, found at Cumae): “From there,” he said, “we sailed until we reached the ancient city of Lamus, Laestrygon.”
(online text: Eng. Lat.)

Fasti: “The Neritian chief (Odysseus) also came: witness the Laestrygones and the shore which still bears the name of Circe.”
(online text: Eng., Lat.)

Strabo, Geography 1.2.9

“[Homer] tells us that king Æolus governed the Lipari Islands, that around Mount Ætna and Leontini dwelt the Cyclopæ, and certain Læstrygonians inhospitable to strangers.”
(online text: Eng., Grk.)

Pliny the Elder, Natural History 3.9,  3.14

3.9: “Next is the site of the Grotto, Lake Fundanus, the port of Caieta, and then the town of Formiae, formerly called Hormiae, the ancient seat of the Laestrygones, it is supposed.”
(online text: Eng.Lat.)

3.14: “We then come to the three rocks of the Cyclopes, the Port of Ulysses, the colony of Catina, and the rivers Symæthus and Terias [quoted on the Polyphemus page]; while more inland lie the Læstrygonian Plains.”
(online text: Eng.Lat.)

Silius Italicus, Punica 7.410

“Carthaginian ships were seen ploughing with their beaks the sea by the shore of Caieta and the bay of the Laestrygonians.”

(online text: Eng., Lat.)

Dictys, Chronicle of the Trojan War 6.5

“Then they had gone to the island of Sicily, where the brothers Cyclops and Laestrygon had treated them with every indignity and where Polyphemus and Antiphates, who were the sons of the former, had killed many of them.”
(online text: Eng. , Lat.)