First off, do keep in mind that Alexander's OTL death spiral was largely caused by Hephaistion's untimely death. Alexander went more or less mad with grief, and even after he recovered his senses, he proceeded to self-destruct in a spectacular fashion. Without Hephaistion's death, it's likely that his death is postponed at least a bit. Of course, for the sake of argument we can just assume he randomly falls ill at around the same time he died in OTL, with fatal results.
Hephaistion would be the obvious choice to be regent in such a scenario. If he's alive when Alexander dies, there can be little doubt (actually, I'd say: no doubt at all) that Alexander would name him as regent. Assuming that, as in OTL, Alexander is capable of speaking on his death-bed. There would be no vague mumbling that could be interpreted as either "to Krateiros" or "to the strongest" (kratistos). It would just be "the regency goes to Hephaistion". Alexander would never in a million years consider anyone else for that position as long as "the other half of his soul" is alive to take the role. Add to that the fact that Hephaistion is married to an Akhaimenid princess, too, and his claim gets even stronger. At the same time, his utter loyalty to Alexander will ensure that he'll never try to take the throne for himself. Hephaistion's support for Alexander's pro-Persian policies of cultural fusion will ensure that any support of Persia as a power block will be thrown behind him, and not Seleukos. Knowing this, Seleukos is in fact likely to support Hephaistion. Perdikkas, too, would likely back Hephaistion. (Perdikkas wasn't out for power, at least not initially: when the troops offered him the crown - persumably with Alexander's son as his heir - he refused and went with regency instead.)
There would no doubt be opponents to a Hephaistion regency, but he'd be in a stronger position than Perdikkas ever was. I imagine parts of the empire would break off. Egypt, Greece, Macedon itself, even... and Chandragupta would probably grab some bits up in the east, as in OTL. Hephaistion would end up in charge of a more powerful version of the Seleukid Empire, which would actually cover pretty much the whole of the old Akhaimenid Empire.
(Needless to say, sudden deaths can change the whole course of history. What I have outlined here merely paints the most likely outcome barring unforeseen twists.)