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Greek city of Boeotia, west of Thebes (area 2).
In mythology, Coronea was the kingdom of Athamas, a son of Æolus and grandson of Hellen. He was married three times and was involved in a lot of troubles with his successive wives, which inspired several tragedies in classical times (none of them still extant) including, by Æschylus, an Athamas ; a play by the same name by Sophocles ; and, by Euripides, a Phryxus and an Ino .
From his first wife Nephele (a Greek word meaning "cloud"), Athamas had a son named Phrixus and a daughter named Helle. But he later abandonned Nephele to marry Ino, one of the daughters of Cadmus, the founder of nearby Thebes. This explains why Athamas was for a while in charge of raising young Dionysus, the son of Zeus and Ino's sister Semele, after his mother had died. With Ino, Athamas had two sons, Learchus and Melicertes, yet Ino was jealous of the children he had had with Nephele and decided to get rid of them. She managed to induce a famine in the country and to make her husband believe that the oracle of Delphi required the sacrifice of Phrixus to end it. But while Phrixus was led to the altar, Nephele gave him a ram with a golden fleece offered her by Hermes, on which Phrixus and his sister Helle could fly away. They flew to Colchis, at the extreme east of the Black Sea, but, along the way, Helle fell in the sea, in a place that was named "Hellespont" in her honor (the strait , today called Dardanelles, between the Ægean Sea and Propontis, today's Sea of Marmara, on the way toward the Black Sea). Phrixus and the ram made it to the court of Æetes, king of Phasis, where Phrixus offered the ram to Zeus in thanksgiving and gave his golden fleece to king Æetes (this is the Golden Fleece the Argonauts came to conquer under the leadership of Jason).
When Athamas learned what Ino had done, he ordered that she be sacrificed in place of Phrixus. But then, Dionysus saved her by surrounding her in a cloud and struck Athamas with madness (or maybe it was Hera, in reprisal against Athamas who had accepted to take care of Dionysus), so that he killed his own son Learchus. When she heard that, Ino took her other son Melicertes and jumped with him in the sea (in some traditions, she is said to have killed him first and jumped in the sea with his dead body). After that, Athamas was exiled from Boeotia and seeked refuge in Thessalia, where he founded another city named Alos and married for the third time.

It is in Coronea that a battle took place in 447 between the Athenians supporting democratic regimes in Boeotia and Boeotian oligarchs led by Thebes. Athens was defeated (Thucydides, I, 113) and Thebes was thus able to reconstruct the Boeotian Confederacy under its leadership.
It is in that battle that Clinias, Alcibiades' father, was killed (see Plato's Alcibiades, 112c).