The best and most reliable Ancient Greek writer who identified and commented on Mycenae.......was Homer and "The Iliad".
Although Homer is not viewed as a Historian and "The Iliad" has often been viewed as the foundation of Western Literature and "Mythology", in reality, "The Iliad", was more of a historical commentary, a type of poetic retrospective sung by the blind Poet Homer, while playing his Lyre/(or Ancient Guitar) on the Aegean island of Chios.
Keep in mind that the content of the "The Iliad" was not necessarily invented by Homer, but rather, a culmination of centuries told tales passed from generation to generation regarding the actual Trojan War from the 1190's BC/BCE. When Homer arrived on the historical scene, it is approximately 400 years since The Trojan War. The generational story of The Trojan War, was rooted in a historical event and the city of Mycenae, was an actual city that Homer and the Greeks of his generation knew of. Remember, one of the central characters of "The Iliad", Agamemnon, was the King of Mycenae and his brother, Menelaus, was the King of Sparta and married to Helen, "Queen of Sparta"-(before she became, "Helen, Queen of Troy"). In other words, the Ancient Greeks, long after the Trojan War, were well aware of the historical and geographical existence of Mycenae. It was not a city shrouded in myth and legend. Even with the archaeological excavations of Heinrich Schliemann, as well as the subsequent translations of the Linear B tablets by Michael Ventris, the Ancient Greeks were well aware of an actual Mycenae-(and perhaps even beyond the Ancient Greeks).
So your best historical reference with regard to the historical origins of Mycenae, comes from a historically sentimental Greek Poet and Singer from 2800 years ago.