Interesting; thanks. I've always had it in my head that Zoroaster was a 6th century BC guy... so it's good to get that cleared up!
Oh come on! 300 was great in how silly it was!
Well mass Greek and Punic colonization was about done by the mid to later sixth century BC - there were still some Greek colonies set up in Italy during the fifth and fourth centuries, and Carthage expanded some where it could, but largely, the great colonization period was over by this point, so I don't think you're going to see major changes there. There is a theory out there that without Persia as a unifying enemy, the Greeks would've never unified amongst themselves... I don't really agree with that, but I'll put it out there.
Instead, what I think you get out of Greece is a stronger and earlier Spartan hegemony - they were the dominant power in Greece by the time of Cyrus, and arguably remained in that position until 370 BC, despite a crippling earthquake, some dynastic conflict, population decline, and several enormous wars with Athens' empire and later Thebes. Athens wasn't very strong during Cyrus' lifetime (even under Pisistratus it wasn't close to how it was once it became a democracy), with a lot of political unrest, and its democracy could very well be butterflied away (which obviously has enormous consequences). Should Athens remain down, only Thebes and (stretching a bit) Argos would be threats to Spartan Hegemony, since Corinth was a part of the Peloponnesian League. Now, Sparta is still destined to fall eventually - primarily because of their difficulties in maintaining the Spartan population, but also because the other Greek cities would start "ganging up" on Sparta until they gain their "freedom" under the direction of some other city - but they were definitely a rising power at the time, and I think it's likely to see them rise all the way to the top without democracy in Athens or Persia building up other states to maintain a balance of power, and for them to maintain that position for some time.
The Greeks in general without Persia might look west a bit more without Persia... without Persia, the "great enemies" for Greeks in general would be Carthage and Lydia (since Carthage has disputes with Greek Sicily and Lydia has disputes with the Ionians), and since Carthage and Lydia are closer in power and prestige than Carthage and Persia, Carthage might get a stronger focus amongst Greeks as the enemy they need to chase around, if this all makes sense.
The big cultural change for Greece and the West is if democracy is butterflied away... I mean, Athenian democracy is just a staple of western culture and history. (Another thought: the Roman Republic might be butterflied too) Without democracy, oligarchies and tyrannies are the staple Greek political systems. As another poster mentioned, Greek philosophy was influenced by Persian thought, so that'll be different. There's also little chance that a Greek conqueror a la Alexander the Great would want to conquer all the eastern states in revenge, since there would be no Persian Empire to get revenge on for the Persian Wars... that means no Hellenism in the East. Carthage would be the strongest cultural power that the Greeks border, so maybe more Phoenician influences will emerge in Greek culture ITTL?