While more can be said on the issue of Alexander's campaigns, /u/xenophontheathenian gave this answer on whether Alexander campaigned further into Europe, how Alexander got his army, and why that army needed to invade Persia. Additionally, /u/Tiako discusses what Greek scholars of the time knew about the world beyond the peninsula.

Funny that you mention it, the very first military campaign of Alexander the Great after he took the throne was in Illyria to the northwest, in what is now modern-day Albania. Or rather it was the second campaign, since he was fighting in the Balkan Mountains (Haemus Mons) of Bulgaria against the Thracian tribe of the Triballi, besieging them on Peuce Island, part of modern-day Romania. Shortly afterwards the Illyrian king Cleitus of the Dardani threatened Macedon, so Alexander marched against him as well, besieging him at Pelion (in what is now Albania). At the same time the city-state of Thebes grew restless and overconfident with the death of Alexander's father Philip II, instigating a revolt from the League of Corinth that was brutally crushed by Alexander. Thus Alexander's first great victories as king were all located in Europe, a year before he set out for Asia Minor to invade the Persian Empire.

I think, logistically speaking, it would have been insane and poor strategy for Alexander to launch invasions against both the Persian Empire AND Western Mediterranean states at the same time. If Alexander had lived until a ripe old age, he could have theoretically made war against Syracuse in Sicily or even Rome's holdings in southern Italy (decades before Pyrrhus of Epirus invaded southern Italy and Sicily). Alternatively, he could have attacked Carthage in the Western Mediterranean, although I don't think he would have ever reached the Greek colonies of southern France (e.g. Massalia) and northeastern Spain (e.g. Emporion). Alexander's empire was already stretched enough as it was, going into the heart of Central Asia and almost touching Xinjiang in what is now modern-day northwestern China.

To be honest a campaign in northern India, after taking the Punjab region of what is now Pakistan, would have made more sense for Alexander's empire. Going all the way west to Gaul (in what is now France) or attacking even further east against the (then unknown) Qin and Warring States of China wouldn't make much sense if we keep in mind the difficulties of logistics in the ancient world.

Rome wasn't built in a day, after all. It took the Romans roughly two-and-a-half centuries to conquer the whole of the Mediterranean, for instance, beginning with the First Punic War.