Aegean coasts of Anatolia

Not likely.

I think that the archaeology of Western Anatolia is rather underdeveloped, at least for such early dates but anyhow we do know that Anatolia overall has been inhabited since Paleolithic times, what makes the Greek origin less likely.

Troy is possibly the most emblematic and best known site in Aegean Anatolia. It dates to c. 3500 BCE, and it is essential in the difussion of Bronze towards Europe, though it seems that suffered several invasions in its long (pre)history, what may imply demographic and specially cultural changes.

In another topic discussing the possible Trojan-Etruscan connection someone posted that recently a seal has been found in troy written in Luwian (Lydian) language, a language that was used among Hittites (along with others) and that was probably dominant in Western Anatolia at that time (2nd milennium BCE).

Another place named in Hittite chronicles is Milawanda, most likely Miletus.

Greeks surely took control of that region in the last centuries of the 2nd milennium, when the Sea Peoples (probably partly Greeks) dominated the Eastern Mediterranean, destroyed Troy and probably also the Hittite Empire, acquiring the secret of iron.

Phrygians (and Armenians) may be connected with this process of Greek and maybe Thracian expansion.

Who said anything about Armenians? The early Armenians at that point were in the southern Caucasus... is there any connection between them and the Cimmerians, the people that ravaged the whole Eastern part of Asia Minor at the time when they drove south? I am not sure... does anyone know for sure?

The Hittite kingdom was destroyed by the Sea People, likely an amalgam of tribes and ethnic groups originating from several islands and coastal areas of the Mediterranean and  involved in an early volkerwanderung in the eastern Med - the only people we know originating from those Sea Peoples are the Philisteans (of the Goliath biblical fame). They attacked every coastal area from the bosphorous to Kyrenaica and they caused enormous fuss and destruction, brought down many kingdoms and even came close to bring down the Egyptian kingdom (there is a rather thorough description of the Sea Peoples and their raids into Egypt in Egyptian sources).  It is quite possible (but definitely not certain) that at least some of those tribes were Greek, and that should be the first Greek expansion in the other side of the Aegean.

For sure the Homeric epics describe - in a semi-mythical context - the first expansion of the Greeks to the other side of the Aegean.

Of course even in historical times the Greeks were not the only people in the western Asia Minor - as a matter of fact, until the hellenization of some of the others inhabitants of Anatolia (notably the Lykians, Lydians and Karians) the Greeks were only the minority.

Also, there are some interesting theories about the (Indoeuropean) Thracian coming from Asia Minor to Europea rather than the other way around (from Thracia to Bithinia). Those theories are mostly speculative, but this is indeed an interesting hypothesis with many side effects.

A short answer to Argentum Draconis: It's safe to assume that the Greeks inhabited Anatolia since the 1300s or 1200s BC and later on they inhabitet mostly two (rather wide, almost the whole coastline) areas: Ionia in the center-north and Doris in the south (including Dodecanese). In historical times we find  also  in the western Anatolia the following people: Phrygians, Thracians, Lydians, Karians, Lykians and a few others. The Greeks were, after the 7th century, the largest individual ethnic group, but they were also a minority when you count all the others together.

Later, most other ethnic groups were hellenized (a process well underway in the 5th century BC - for instance, Herodotus was of mixed Greek-Karian ancestry) and in the AD years we find little or no traces of the local languages and distinct culture.

Does this cover your question?

Originally posted by Argentum Draconis What  Armenians has to do with this matter? They were far away. And also didnt Assyerians destroy Hittites?

Some (Herodotus?) suggest that Armenians were Phrygian colonists, there are other theories but I can't be sure of which is the correct one.

Assyrians didn't destroy the Hittites as far as I know. The common understanding is that the Sea Peoples or some associated nation like Phrygians did it. Assyrians probably benefitted from the power vacuum but their rise only happened later on. (At least as far as I know).

Checking some resources I ended in the new version of Wikipedia's articles on Hittites (it seems there's some activity going on in decifering texts that is adding relevant info on that obscure period). The article History of the New Hittite Kingdom says:

Hattusili's son, Tudhaliya IV, was the last strong Hittite king able to keep the Assyrians out of Syria and even temporarily annex the island of Cyprus. The very last king, Suppiluliuma II also managed to win some victories, including a naval battle against the Sea Peoples off the coast of Cyprus. But it was too late. The Sea Peoples had already begun their push down the Mediterranean coastline, starting from the Aegean, and continuing all the way to Philistia -- taking Cilicia and Cyprus away from the Hittites en route and cutting off their coveted trade routes. This left the Hittite homelands vulnerable to attack from all directions, and Hattusa was burnt to the ground sometime around 1180 BC following a combined onslaught from Gasgas, Bryges and Luwians. The Hittite Empire thus vanished from the historical record.

By 1160 BC, the political situation in Asia Minor looked vastly different than it had only 25 years earlier. In that year, the Assyrians were dealing with the Mushku pressing into northernmost Mesopotamia from the Anatolian highlands, and the Gasga people, the Hittites' old enemies from the northern hill-country between Hatti and the Black Sea, seem to have joined them soon after. The Mushku or Mushki had apparently overrun Cappadocia from the West, with recently discovered epigraphic evidence confirming their origins as the Balkan "Bryges" tribe, forced out by the Macedonians.

A large and powerful state known as Tabal had occupied the region south of these. Their language appears to have been Luwian, related to Hittite, but usually written in hieroglyphics instead of cuneiform. Several lesser city-states extending from here to Northern Syria also used Luwian, although they are sometimes known as "neo-Hittite". Soon after these upheavals began, both hieroglyphs and cuneiform were rendered obsolete by a new innovation, the alphabet, that seems to have entered Anatolia simultaneously from the Aegean (with the Bryges, who changed their name to Phrygians), and from the Phoenicians and neighboring peoples in Syria.

Ironically, the language of the Lydians, spoken in the West of Asia Minor until the 1st century BC, was apparently a linguistic descendant of Hittite, and not Luwian. This and the fact that one of Lydia's kings known to the Greeks bore the Hittite royal name Myrsilis (Mursilis) may indicate that this state was the purest cultural and ethnic continuation of the former Hittites. The last trace of this language persisted until the 5th century AD, according to some Church Fathers, when it was known as the tiny dialect of Isaurian, spoken in only one or two villages.

I kept the last paragraph because it seems relevant. I always thought that Lydians spoke Luwian but it seems it's not the case. The author of this article seems to identify pretty well the origin of Phrygians, something I thought it was more obscure.

Originally posted by Argentum Draconis Who are those sea peoples and how do they crush such mighty empires? Where do they come from?

That's another story but it seems that they were mostly Greeks (Lydians too and possibly other peoples - Etruscans? Sicilians?). It also seems that the Hittites were in a low moment. They were able to create outposts in the Levant (most famous are the Philistines) but they failed in conquering Egypt, despite the fact that Egyptians only had Copper Age technology. With that backwad technology Egyptians had also stalemated with Hittites at Kadesh not long before.

There's a recent topic somewhere on the Sea Peoples, quite interesting. Use the search feature.

Hittite inscriptions indicate that the Arzawan state (known since the 17th century BC) had a capital at Apasas which was described as being next to the sea.  Based on several sources, some Hittitologists identify Apasas with Ephesus.  We therefore have a Luwian presence in the later region of Ionia.  Hittite sources also mention other peoples such as the Lukka, Karkisa, and Masa which seem cognate with the classical Lycians, Carians, and Lydians or Mysians (whose founder was said to be Masnes) dating from the 15th century BC.  Since we know that the Lycians spoke a Luwian language and the Carians, perhaps so, and the Lydians a Hittite dialect, and since the archaeology of the region of western Anatolia was persistently of the same culture, it is reasonable to assume that the Luwians were on the western coast first.  Miletus presents a special case in that it was originally a Minoan settlement but became a Mycenaean one.  Miletus, as well as two sites at the southwestern coast of Anatolia are the only known true Aegean settlements during the Bronze Age.  The western coast of Anatolia with few exceptions was mostly Luwian.

It was published in Archeology last year.. I managed to find the article here