Stoyan Shentov’s answer that Greeks ultimately came from the Proto–Indo-European homeland is not unreasonable; but we can answer the question more proximately, as what the likely homeland of the Proto-Greek speakers were. (And of course, the Proto-Greek speakers did not come into terra nullius: they intermarried with the Pelasgians or whatever they were who were already living there.)
The Proto-Greeks probably arrived at the area now called Greece, in the southern tip of the Balkan peninsula, at the end of the 3rd millennium BC. The sequence of migrations into the Greek mainland during the 2nd millennium BC has to be reconstructed on the basis of the ancient Greek dialects, as they presented themselves centuries later and are therefore subject to some uncertainties. There were at least two migrations, the first being the Ionians and Aeolians, which resulted in Mycenaean Greece by the 16th century BC, and the second, the Dorian invasion, around the 11th century BC, displacing the Arcadocypriot dialects, which descended from the Mycenaean period. Both migrations occur at incisive periods, the Mycenaean at the transition to the Late Bronze Age and the Doric at the Bronze Age collapse.
An alternative hypothesis has been put forth by linguist Vladimir Georgiev, who places Proto-Greek speakers in northwestern Greece by the Early Helladic period (3rd millennium BC), i.e. towards the end of the European Neolithic.