The Greek city-states were free to go back to their endless wars against each other, weakening themselves to the extent that Macedonia was able to dominate them until Rome progressively took over two centuries later.
Athens and Sparta .
Which Persian War? Persia fought the Greek city-states over 2,000 years ago; is your question regarding that Persian War?
The Persian Empire fought the Persian War against a couple of hundred Greek city-states over fifty years 499-449-BCE.
The Persian War 499-449 BCE.
The Persian Empire versus coalitions of Greek city-states led first by Sparta, then by Athens.
Persian War: The Greek cities of Asia Minor provided a third of the Persian navy for the 480 invasion of southern Greece. The Greek city states of central Greece provided a substantial part of the Persian army which fought the southern Greek armies. Peloponnesian War: Athens and the cities in its empire fought the mainly Peloponnesian cities led by Sparta.
The Persian Empire versus varying combinations of Greek city-states.
Athens and its empire versus the Peloponnesian League led by Sparta.
The Greek and Persian War started in 499 B.C.
When was the 'First' Persian War.
Which particular war? The Persian what?
Persian War: a coalition of the southern Greek city-states versus an expeditionary force from Persia with its local Greek allies. Peloponnesian War: the Athenian league/empire versus a mainly Peloponnesian League led by Sparta.