How could the Greeks build so many cities around the world (Constantinople, Alexandria, Athens, etc.)?
Compared to other ancient peoples, the ancient Greeks were highly urbanized. A political system that became increasingly common was the city-state, the "city-state" that established the main city, usually a walled hut. The land around it is usually not very large, and there are enough farms and villages around the city-state that a man can go to his farm and may walk back on the same day, even if it is close to the border. Even in areas that were initially tribal in the late Classical period, they began to organize into cities, often through a process called unionism.
In the map above, we see the ancient Greek regions that first organized themselves into cities. By the late Classical period, most areas marked as tribal were highly urbanized. Even mountainous Arcadia has large cities, which literally mean "big cities," Megalopolis. This makes the region even stronger. For example, when Epameinondas defeated the Spartans, he helped the Messenian helots establish a large city-state, and Messene was now strong enough to resist the nearby Spartans.
Messene (pictured above) is obviously much better than the village of Helot, which works in the fields of the urbanized Spartans.
The city-state was also the ideal form of government for the Greek colonies. Greek cities would disperse their surplus population and establish a new independent state where they found good places. But considering that the settlement may be inhabited by hostile foreigners, they usually just build a city and farm nearby. For these Greeks outside mainland Greece, it is normal to build settlements like they once were their home. In this way, most of the Mediterranean coast was settled by the Greeks. Although they were excellent sailors, they would travel and trade in these cities.
In any case, a city like Mason above would be a better place to trade. In the bazaar of the central square, all the shops are gathered together, so it is easier to do business, just like shopping in a big supermarket with a wide variety of products together or in some shopping mall of a big city, rather than going to a village to buy apples, one to buy pottery, one to buy olives, and then go to the port to buy fish.
After the rise of Macedonia and the conquest of Alexander the Great, larger forms of state began to prevail. Nevertheless, Alexander, a man born and raised in a Greek city and educated by Aristotle, was the one who studied the constitution and formation of the city of Athens, and he would continue to build a whole bunch of Greek cities in his empire, most of which they called Alexander.
As I described in my answer, the cities were originally built as forts, with senior soldiers and camp followers as well as locals from neighboring tribes. As cities prospered, Greece has always had the problem of overpopulation, but there is not enough space and fertile land to feed them. The second and third sons would have no farms and would have to find a job that was usually a mercenary in the late Classical era, which led to the anger of the Greeks. Isocrates had suggested to Philip (5.122) that Alexander finally accomplish the following:
Use these forces to fight the barbarians, to take away from that empire all the territories I have just defined, to free these homeless wanderers from the diseases they have suffered and to the people they have inflicted on others, to gather them into cities and to use them to fix the borders of Greece, to make them a buffer state to protect us all. Because doing so will not only allow them to prosper, but it will put us all on a safe footing.
Conquering this land, Alexander moved all the homeless wonders to his places like Alexandria.
Even though there are only a few cities in that particular country, I said in a recent answer that there are hundreds of thousands of Greeks who have settled in Egypt. Therefore, they are enough to build large cities around the world, but also have the capacity and need to do so, because the cities of the Greek mainland are not enough to feed them, for example Egypt is a better place to grow grain.