Four kinds of Amazons should be distinguished in accordance with Greek sources:

Cappadocian Amazons

They lived in Cappadocia, an area of the northern Anatolia (modern Turkey). Their capital was Themiscyra on the river Thermodon, and they are known mainly from Greek mythology. They are also called The Amazons of Anatolia.

Scythian Amazons

They lived in Scythia (modern Ukraine and southern Russia) and in the whole space of Eurasian steppes. They are known mainly from reports by Herodotus and Hippocrates . Some shade them leaves in folklore of Eurasian peoples. For instance, I can name polyanitsas ('steppe females') and Virgin Sineglazka ('blue-eyed female') of Russian folk tales, Ochi-Bala of Türkish epos. Their remains are also find by archeologists, see Ancient Graves of Warrior Women Offer Hints of Amazons.

Libyan Amazons

They lived in Libya (northern Africa). Diodorus Siculus has written the most important report of Libyan Amazons. There are also some remarkable indication of Libyan Amazons' heritage in culture of Berbers — later local inhabitants of northern Africa.

Aegean Amazons

Significant but unclear traces of the Amazons exhibit in Aegean basin (proper Greece). So the main shrines of warrior goddess — Athena and Artemis — stood in this area (Athens, Delos island, Ephesus). Also actions of many myths on these goddesses and proper Amazons took place in this area. These myths explained this with invasion of Amazons. However, there are reasons to think that, conversely, the Amazons were exiled from this region by the peoples who took part in forming later Greek nation.

Several important facts indicate identity or very close relationship, at least, of the Cappadocian Amazons and Indo-Europeans — hypothetic people known through the reconstruction of its language from multiple derived languages comprising Indo-European family. The width of spreading of these languages displays cultural potential of their ancestor nation.

So, the homeland the Amazons is practically the same as country of Hittites — the most archaic Indo-European people. Furthermore, Hittites was overwhelmed by so-called 'peoples of sea' surely identified with Achaeans, and the Cappadocian Amazons were defeated by heroes of Greer mythology — the same Achaeans. Also time of existence of Hittite empire practically corresponds well to the probable time of existence of mythological Amazons.