this seems to be a really obscure subject in Athenian history

The Panathenaea is, apart from the festival to Olympian Zeus and maybe the poorly-understood Eleusinian festival, probably the single-most discussed and studied festival of the ancient world. Traditionally the festival was founded by Erichthonius, Athens' mythical king, although Plutarch and Pausanias knew of traditions in which Theseus either instituted or reorganized the festival. I'm not sure where you're getting June or July from; the Panathenaea was celebrated in Ἑκατόμβαιον, according to the late scholar Aristides in commemoration of the Minotaur. The precise date of the Panathenaea migrated according to our modern calendar, as the Athenian festival calendar operated according to a very complicated series of calculations with the moon, sun, and seasons. Two Panathenaeae existed, a "Greater" and "Lesser" version, differing only in the form of the festival. The Greater Panathenaea, instituted probably sometime in the sixth century (like all the trappings of the Classical festival), was held every four years and included an athletic festival and other competitions. The Lesser Panathenaea was held in the intervening four years and did not include the magnificent competitions of the Greater Panathenaea. The Greater Panathenaea, like many religious festivals occurring at Olympiads (i.e. every four years), was a panhellenic event, although naturally one greatly focused on the city itself. At the Greater Panathenaea individual athletic and rhapsodic competitions existed, like those at Olympia, Nemea, Isthmia, and the Pythia (the four "Panhellenic" festivals), as well as team competitions like torch relays probably limited to Athenian citizens competing alongside their φυλαί. Both Panathenaeae included the ritual procession through the city, beginning at the Ceramicus and ending at the temple, civic sacrifices, choirs of boys and girls singing throughout the night, and of course the presentation of the cult statue's new πέπλος