I'm relatively biased on this matter; the entire basis of my timeline is on a surviving Argead Empire and its ramifications.
Rather than just plug it, this is the direction that I went; I felt that, given a more direct policy of integration, over time the Persian ruling class and the initial Macedonian aristocracy of the Empire would merge. In my timeline this eventually manifests in the Argeads themselves touting clearly Greco-Persian tendencies. However, the eventual growth of Greco-Persians and other fusion cultures would probably distance them significantly from any Greeks back West with rather different attitudes and no such fusion. In particular, even if Macedon remained part of the Empire it would likely grow completely disaffected from the Argeads if they persified over time.
A strong Argead Empire either leads to the conquest of Egypt, or a detente- the OTL Seleucid-Ptolemaic wars seem rather unlikely when the Argeads have the added claim of a) semi-genuine legitimacy and b) probably even greater resources to work with, though the early Seleucids were hardly destitute either. If a detente, you'd end up with quite a stable Eastern Mediterranean. If conquest, then the east Mediterranean is an Argead lake anyway and is similarly going to be fairly peaceful. Egypt denied expansion in the Mediterranean, if it remains independent, will likely turn elsewhere. That leads to Greek material culture becoming common across probably East Africa and Arabia (and OTL commerce was enough to result in the creation of imitation Athenian drachmae in Arabia).
A strong Argead Empire, if it's ruled relatively sensibily, will be unable to directly expand into Italy, or possibly as far as Greece without pushing things too far. It's likely to create a circle of client states around it, just as the Achaemenids for a time had several client states including Macedon itself. Rome, if it isn't butterflied away, is likely to figure into these calculations one way or the other. Epirus likewise. Any non-Greek state that's made a client in such a way is liable to either react against the perceived foreign influence.
However, if there is anything resembling an OTL succession war, the fallout from that could still result in an Argead Monarchy but a very different post-war climate in Europe. You might end up with Epirus conquered, with Greece remaining part of the Empire, or conversely with all of this territory completely lost. The question of Greeks in Asia and Greeks in their homeland going in completely different directions is again raised.
Arguably, the period likely to make the most significant difference to Hellenisation/fusion cultures is a) the start, based on whatever Alexander/his successor does, and b) starting in the 160s BC. The 160s is when the Seleucid Empire was clearly on the downswing, and around 140 is when the Greco-Bactrian Kingdom was destroyed. The effects of surviving Hellenistic states past these key dates is likely to have a significant effect on the eventual cultural evolution of those states. Even in OTL, the after-effects of Greek culture in Central Asia and the Near East echoed for several centuries after they were no longer in control.