The conventional answer is Salamis, when the Persian fleet sailed into a narrow straight where they couldn't properly maneuver and the Greek allies captured and destroyed so many of their ships that the fleet had to abandon Greece altogether. With the navy gone, King Xerxes fled back through northern Greece and Thrace with most of the initial (second) invasion force. The journey through Thrace was terrible for the Persian army. A combination of the missing fleet, Thracian rebels, and Thracian loyalists being unprepared for the sudden arrival of the Persian army in early winter yielded few supplies but lots of disease.
That said, I don't want to talk about Salamis. Neither the battle itself nor its immediate consequences are particularly complicated. The presentation of Salamis as a great turning point is largely the result of Herodotus' Histories identifying it as the great Athenian victory in Greek territory and a harbinger of Athens' emerging naval power.
Determining a more accurate turning point really depends on how you define "the Greco Persian wars?" The typical definition of the two major Persian confrontations with Athens in Greek territory (the landing at Marathon in 490 BCE and Xerxes' Invasion in 480-479) is fine if the two early invasions that the Greeks thought of as attempts to conquer their land are all that you care about.
However, it's hardly the full scope of Greek wars with the Persian Empire. Xerxes' Invasion isn't even the end of continuous hostilities. The Greeks went on the offensive from 479 onward, first under the full auspices of the Hellenic League (including Sparta and its Peloponnesian allies) and then continuing on under the Athenian-led Delian League for decades. From my Achaemenid Studies perspective, approaching things from the Persian side rather than the Greek, I think there's a reasonable argument to be made that there's a nearly-continuous conflict from the Ionian Revolt in 499 BCE all the way to the end of the Corinthian War with a peace treaty, sometimes called the King's Peace, dictated by Artaxerxes II in 387 BCE. At the very least the Delian League's wars with Persia are a direct continuation from Xerxes' Invasion all the way to 449.
In the narrowest view, just focusing on the invasions of Greece in the 5th Century BCE, I think the Battle of Plataea is much more of a turning point than it typically gets credit for. Salamis is great and all, certainly preventing the Persians from taking any more ground, but the Persian army that remained in Greece still had free reign of the country north of Corinth in Spring 479. Mardonius led his troops south and re-burned Athens, sending the inhabitants back to their earlier refuge on Salamis as soon as the campaign season began. Reinforced by pro-Persian Greeks and Thracians, descriptions of the Persian camp and modern analysis suggest he commanded between 70-100 thousand troops, woefully outnumbering the Athenians while Sparta and the Peloponnesian League refused to march north and leave Corinth vulnerable.
It took months for Athens to persuade them to go on the offensive, but when they did the full force of the Hellenic League was able to muster around 80,000 soldiers, giving them somewhere between a numerical advantage or near-parity to the Persians depending on the modern estimates. Only then were the allied Greeks able to defeat the Persians in open battle and prevent them from running rampant through Greece. Add in a few tactical errors and a dead commander on the Persian side and it was an overwhelming Greek victory that sent the surviving Persians fleeing home, functionally abandoning most of their European territory along the way. There wasn't really any kind of turning point between Mardonius getting to burn and pillage Athenian territory as much as he wanted and a complete Persian rout. No Persian troops set foot in the Greek mainland under arms again until 393 BCE.
According to Herodotus, the Battle of Mycale occurred on the same day as Plataea, and it is potentially a more significant turning point than either of the battles in Greek territory if you take a longer view of the Persian Wars. Once the Peloponnesian city-states agreed to go on the offensive, the Hellenic League's fleet (overwhelming composed of Athenian ships) went hunting for the Persian navy that had fled the previous year. They tracked them down to the mouth of the Maeander River, in the shadow of Mt. Mycale. The Persian ships were beached and the Greeks landed before the Persians could get back in the water. The two naval forces staged a land-battle on the beach, with the Greeks driving the Persians into the mountains and burning the entire Persian fleet on the sand.
It took decades for the Persians to rebuild a large enough navy to really challenge Athens at sea again (in part because when they got close an Athenian force repeated the same basic events as Mycale in the Battle of the Eurymedon). Athens had free reign of the Aegean for the next 24 years, and used that to capture almost every Greek city in Persian territory while intermittently raiding Persian-ruled cities in Phoenicia (and presumably burning their shipyards).
The tables turned again in 460 BCE when Athens attempted to support the would-be Pharaoh Inaros II in his rebellion against the Persians in Egypt. This turned out to be particularly poorly timed because the bulk of the Athenian fleet wound up embroiled in a 4 year siege of Memphis from 459-455, just as the First Peloponnesian War was kicking off in Greece. The Persian commanders in charge of western operations, Artabazus and Megabyzus, allowed the siege to continue uninterrupted because Memphis was nearly impregnable so-long as southern Egypt remained loyal. That gave Megabyzus time to rebuild the Persian navy and train his troops, sweeping down the Nile and coming up behind the Athenian ships and Egyptian army in 455, breaking the siege and scoring Persia's first significant naval success against Athens. Athens made one last bid for seizing Persian territory with an invasion of Cyprus a few years later, but the restored Persian fleet was able to fight them off, especially when the Athenian general Kimon died on the island.
It was enough to bring both sides to terms, with King Artaxerxes I agreeing to cede control of the cities Athens had already captured and keep his troops away, and Athens nominally agreeing to stop conquering unwilling Persian territory by 449 BCE, the supposed Peace of Callias.