Arabia was certainly his first order of business.
Then, he might either head West, or give a second try at India. In both areas I think he'd face serious challenges. In the West, mostly because he, being Alexander, could overreach; let's say he takes Carthage and Sicily (which is probably possible), do you think he'd resist walking on the westernmost shores of the known world, if not for prestige reasons? He'll probably try to go all the way to the Atlantic. He might even manage to do that and get his overlordship somewhat recognized by Maurians, Iberians and other local peoples, but it would not be a walkover.
Italy might be tough, but there are Greek cities there, and probably he'd want to "protect" them and impose some sort of suzerainty over the Italics. If he does not make excessive demands, he could get that, although Rome and the Samnites both would not take that kindly.
India is a much harder proposition. Indus valley may be realistic, but anything beyond that would mean logistical and political challanges that he probably wouldn't be able to overcome (and there's the different disease enviroment too). Moreover, in India he could face a general may outclass him, younger, and with roughly equivalent resources at his disposal. Now, I guess that in terms of military history, Alexander vs. Chandragupta is probably the battle.
Politically, his Empire was overstreched as is IOTL; it would be difficult to keep the Macedonian generalship on a short leash because of sheer distances. Rebellions would be a common problem. He'd need to expand the powerbase, which he sort of realized when he tried to integrate the Persian aristocracy into it, but was not taken kindly by the Macedonians or the Greeks. The Greek city-states too are a problem - a lot of them weren't exactly fond of Macedonia to begin with.
It may be worth noting that the Kingdom of the Cimmerian Bosphorus had a civil war around 310 BC. That could offer Alexander a neat chance to meddle in the Black sea region if he lives that long.