I know that the Greeks had reached as far North as Ischia pretty early on; there's a cup bearing a Greek inscription found on the island dating from the 8th c. BC. Ischia is off the coast of Naples, a comparatively short distance away from Rome. Why did the Greeks (to the best of my knowledge) never reach what is present day Lazio?
In brief, because their increasing expansion challenged both the Etruscans whose sphere of influence covered much of northern Italy and the Carthaginians, who feared losing profitable trade to the growing Greek presence in Sicily and southern Italy.
Tensions eventually led to an Etruscan-Carthaginian alliance and heavy fighting around 540 BC, notably at the Battle of Alalia, where a joint Etruscan-Carthaginian fleet defeated a Greek fleet. This halted Greek expansion into the western Mediterranean, isolating Massilia and strangling the small Greek colonies in Spain.
Alalia led to a series of wars between Carthage and the Greek city-states of Sicily. Hiero, the tyrant of Syracuse, won important victories over Carthage in 480 BC and the Etruscans in 474 BC. This eroded Etruscan influence and allowed the frontier settlement of Rome to rise up and begin consolidating power in Latium.