[1] A Nereid or sea-nymph, attested from Homer (Iliad 18.45: Web address 1) onwards. Best-known for the story, first ascribed to the dithyrambic poet Philoxenus of Kythera (phi 393), of the love of the cyclops Polyphemus for her (see theta 475). Philoxenus was writing in the court of the Syracusan tyrant Dionysios (delta 1178), and the Homeric cyclopes were thought to have lived in Sicily, so Philoxenus' apparent innovation in the myth was possibly motivated by local concerns. The story subsequently became popular among Hellenistic poets, chiefly through the agency of the Sicilian Theocritus. Usually it is Polyphemus who pursues Galateia, unsuccessfully (e.g. Theocritus, Idyll 11), but a parallel tradition develops in which Galateia is at least tacitly receptive to his advances (e.g. Theocritus, Idyll 6; Nonnos, Dionysiaka 39.257-64, 40.555), and Appian, Illyrica 10.2 makes her and Polyphemus the parents of several children, including Galas, the eponymous ancestor of the Galatians. Ovid, Metamorphoses 13.738-897 is the earliest surviving account to include the character of Acis, a youth to whom Galateia is devoted until he is killed by Polyphemus and transformed into the Sicilian river that bears his name. This addition to the story did not, surprisingly, have much impact on the later tradition, although there are a couple of artistic representations of the story showing a figure who could be Acis (LIMC 5.1.1000-05: #29, #47). See generally OCD(4) s.v. (p.599).
[2] In central Asia Minor (modern Turkey). Also a Roman province of that name. See generally OCD(4) s.v. (pp.599-600). The most likely reason for mentioning it here is that in late Greek, apart from accent, the name Galateia and the region Galatia were homophonous, but see also note 1 above for the putative connection between Galateia and Galas, the eponymous hero of the region.
[3] Not a very common one, but see for instance Supplementum Epigraphicum Graecum 11.1009 (on a rock-cut inscription from Messenia, probably third century CE).