Early legionnaires were not trained professionals: most of them were called upon on a conscription basis. Their tactics and strategy consisted of: "Go forward." The lines of the Legion were easy enough to understand: 1st line are unexperienced, 2nd line more experienced, 3rd line are the crack group, and perhaps the phalanx after that. So they essentially steamrolled their lesser opponents in the Italian peninsula.
Had Alexander, a very skilled tactician and strategist, been as healthy as he was when he conducted the campaigns in the east, would no doubt have given the Romans serious trouble.
As Gaius Octavius mentioned, the Mediterranean peoples may have joined up against Alexander, but in all likelihood the biggest problem that Alexander would have faced is the terrain. The many different people that lived in the Mediterranean, were likely to have joined up with Alexander, as they did with Hannibal on his march to Rome.
The challenging terrain to navigate most likely would have been an interesting factor for Alexander to contend with. Also, Alexander's reliance on the cavalry may not have been effective as Hannibal's mixed infantry/cavalry tactics. Remember Italy is a mountainous country, protected by the Alps.
To us, now, crossing the Alps creates awe. Then, the Alps must have been seen as an insurmountable obstacle.
[nr]
I would say that had Alexander been at full health (mental and physical) and was determined to go West, he would have enlisted his expanded expeditionary forces from Persia (as suggested by Segestan), but travelled by naval forces or land march hugging the coastline. The Roman Republican leadership was not exactly united or designed for warfare, as evidenced by Hannibal's first years of invasion. The division would have proven ruinous to the Roman Republic had Alexander been their enemy as well.
It may have even been possible that Carthage, depending on when Alexander engaged in this hypothetical Western Campaign, would have allied with Alexander against Rome. Or perhaps Alexander would have gone after Carthage first. Who knows. THis is one of the things that historians debate ad nauseum like whether China would have dominated the world post-1500 had they continued with their maritime expeditions.