Most people believe that the Roman legion was very much superior to the Greek and Macedonian phalanx, and OTL history seems to prove that. So It sems rather important to break Roman power as early as possible, perhaps even by Alexander himself.
Rome did not start conquering Italy with Legions. Their first armies used the phalanx tactics like most other city states, until the manipular flexibility of the Samnites showed them how awful their old Hellenic (not Macedonian) style phalanx tactics were. They adopted the manipular system after Alexander had conquered most of the Persian Empire.
Second the Romans never actually fought against an Alexandrian Macedonian Phalanx were the sarrisas held the centre, the Hypapists held the flanks of the Phalanx and the cavalry waited at their flanks to flank the opposition.
After Alexanders death the Successors did away with the Hypapists gradually and concentrated on the strong phalanx when their wars became Phalanx against Phalanx and not seeing how useful a strong flexible infantry unit were until they came upon the Romans.
Many of the battles held up as triumphs of the Legion over the Phalanx such as Pydna or Magnesia are actually examples of how you
should never use a Phalanx.
At Pydna the Phalanx army had split in half to march down to meet the Romans from their rocky high ground.
You never divide a phalanx. Its unbroken wall of sarrissas are to keep the enemy from breaking your line. Even the Roman general was quoted to have said "Anyone who says they saw that wall of spears approach and did not break out a cold sweat is a liar."
At Magnesia the strong central hammer of the Phalanx was again broken by Antiochus' love of elephants. Hannibal must have pulling his hair out watching it play out. Once again
you never divide a phalanx.
If you are holding Pyrrhus up as the reason a Phalanx would never win against Rome...he lost most of his army in a storm crossing over from Hellas and still he fought the Romans to within a few hundred miles of their capital. They were on the verge of surrendering to him before a speech from an old blind Senator steeled their resolve to "Never submit to Kings!"
Imagine what Alexander would do in comparison with his immense Empire to the pathetically tiny kingdom of Epirus achieved. Heck Antigonas Monothalmus would probably take Italy given he was a far superior general.
To get back to the original OP.
Rome (and much of northern Itlay) would likely be a ruin, destroyed by the Cimbri and Teutones and subsequent barbarian migrations.
The Adriatic Sea would be a haven for pirates scuttling between the Dalmatian isles, the likes of Teuta of Illyria, Kleomynus and a a guy during the Social war of Italy called Agamemnon.
Before Pyrrhus went to Rome a violent Spartan prince called Kleomynus* was exiled for his abusive and horrific outbursts of rage against his family and fellow citizens. He became a rather nasty pirate lord in the Adriatic Sea demanding hundreds of virgin girls and boys as tribute from cities that he constantly attacked. Imagine a Spartan descended Pirate kingdom among the Dalmatians harassing shipping and generally being a nuisance for centuries with no strong power to stamp it out.
Southern Gaul would likely be under the control of the Arverni God Kings, who were on the rise before Rome broke their power and allied with their rivals the Aeudi Confederation. Spain would have been split between various tribes but perhaps the several Carthaginian cities would likely become centred around their new capital of Gades on the Pillars of Heracles and begin to spread outwards.
With the invasion of Barbarians from the steppes the Dacians and other Danube dwelling barbarians would be fleeing from the steppe Hordes into the Mediterranean, bringing with them the word of their One god Zalmoxis and his Belagines (the Beautiful Laws) by which they live. Perhaps their priests could find willing followers among the Hellenics and other barbarians.
The Huns would concentrate on invading the Middle East were all the Imperial wealth is located, through the Caucasus, as the Scythians had done before them (getting all the way to Israel). The huns had invaded the middle east just before Attila came to the forefront. Likely if there is one huge Empire sprawling across three continents it will be hard to defend, especially if it collapses under infighting as it would more than likely.
Carthage would continue to be trade hub between the East and West Med raking in money without a pesky Empire to uphold. Perhaps the waning Imperial authority would cause it to break away again.
Hellas would be an irrelevance, a ghost of a civilisation. As the Macedonian authorities demand more and more settlers (there are only so many Macedonians) to create their colonies in the East , the citizenry would drain and the once great theatres and agoras of Athens and Pella would be almost empty as people leave for a better life in the East.
*Kleomynus rather than Kleomenes.