If Arnold Toynbee is to be believed, Alexander living a few decades longer would eventually result in a Hellenic world-empire under the Argeadic dynasty. (Spoiler alert: Toynbee, for all the respect he is due, is NOT to be believed on this. His excercise in alternate history is a truly ludicrous Alexander-wank that makes the Draka look very realistic and modest.)
Of course, I do in fact agree that Alexander living a few decades longer and leaving his empire to a succesful heir is the best way to really wank Hellenism as much as you realistically can. It would never be world-wide, but you could easily imagine one of Alexander's heirs eventually conquering India after all (with Alexander himself having already taken Arabia and the western Med)-- thus creating an empire that stretches from Gibraltar to Bangladesh (to use the OTL names), and potentially from the Crimea to Yemen, or even including "Azania" (the Greek name for east Africa, where Greeks actually traded during the Hellenistic age). But I don't really see it expanding beyond such borders. One culture imposed on the whole world just seems pretty hard to do...
I think that's pretty much the best case scenario for spreading Hellenic culture. Of course, if we look at Alexander's intentions, it would be a hybrid culture everywhere. Greece itself would be changed by the other cultures just as much as those cultures would be affected by Hellenism. (Of course, one might say that this is exactly what makes the idea so captivating; I certainly would say so!)