It depends on what you mean (or where you mean) by "Greeks". The Greeks had many city-states located in Italy proper, including Tarentum and Naples. The Romans called southern Italy "Magna Graecia" meaning "Great Greece" because of the large population of Greek city-states in the boot of Italy.

The Romans gained much from their Greek neighbors in the early period of the Republic. The Greeks' influence on Rome was in the form of Art, Writing, and Religion. The Greeks were soon to be at odds with the Romans. There was a war in 281 BC where Pyrrhus from Epirus (A Greek city-state from mainland Greece) invaded Southern Italy with the help of Tarentum. The war he had with Rome contained a battle where Pyrrhus won, but sustained extremely high losses, coining the phrase "Pyrrhic victory" meaning the similar outcome.

So, Rome's relationship began as neighbors to the Greeks, but resulted (like almost all of Rome's neighbors) in a bloody war. Rome did go to the Balkans much later as well.