Quite a lot. Indeed, most large cities in the Mediterranean world got that way because they were able to exceed the production limitations of their surrounding hinterland by importing food. Few cities, even in the most productive regions, could sustain a particularly large population from their local area alone. Even smaller cities had difficulty sustaining themselves. Athens, while a decently large Classical city-state, was not particularly large compared to contemporary cities in the east or later cities in the Hellenistic and Roman Periods. With a population of probably only a few hundred thousand, and only something like 20,000 adult citizen males (estimates vary wildly, and I'm hardly on top of them) in the 5th Century Athens was absolutely dwarfed by the likes of Rome, Alexandria, Roman Carthage, or Antioch. But even the Athenians were forced to depend heavily on imported grain, receiving hundreds of thousands of μέδιμνοι. Much of this import was during the Peloponnesian War, when the city was cut off from its hinterland, but the Attic countryside could not supply the city during normal periods without imported aid in any case.

Furthermore, grain import was crucial to protect cities from famine. Prior to the Green Revolution farming was a much more risky ordeal. Even a slight dip in a region's temporary productivity might have devastating effects for cities that were packed full of inhabitants. The already strained food supply of large cities in antiquity could completely snap in the face of a poor harvest. Famine was a big fucking deal, and grain import helped provide a buffer against that sort of thing. Grain import allowed excess grain to be easily stockpiled, and it also ensured a steady supply of food even when the local countryside could not produce, even if that hinterland was in fact capable of providing for the city.

Of course the most notable example of a city that survived on the grain trade is Rome itself. With at least a million inhabitants by some time in the 1st Century, B.C. the city was totally unable to be provisioned by the local Latin countryside, and when the grain trade broke down in late antiquity the city's population dwindled rapidly. Imports from Campania and fertile Apulia (for real, go to Apulia some day, it's just wheat farms as far as the eye can see) were originally enough, but soon the city was demanding more grain than could be reasonably supplied for cheap. That's another thing, cost. A city of any reasonable size might be able to provision itself via overland routes, but it was too expensive to do so. It cost vastly less to haul grain by sea from Sicily and Africa, which were more productive in any case, than overland from Apulia or Campania. The acquisition of provinces allowed the city to provision itself at previously unthinkable levels, with the population rising in tandem. The Roman grain import, obtained largely through provincial grain taxes, was absolutely enormous. Sicily paid 3 million modii of grain a year, a tenth of its total production--more could be purchased if there was need, as was the case in 73 when nearly 4 million more modii were purchased to offset famine. According to Josephus the province of Africa alone supplied the city for eight months per year. Pseudo-Aurelius Victor reports that Egypt under Augustus supplied the city with a whopping 20 million modii of grain per year. The overseas grain trade was so crucial to the city that threatening it was tantamount to putting the city under siege. When the Cilicians disrupted the grain trade from Sicily and Africa the Romans were forced to grant Pompey an extraordinary magistracy to clear them out--Cicero reports that the day that Pompey's magistracy was enacted grain prices plummeted as traders began to become more assured of the survival of their cargo.

Much the same could be said about other large cities. Constantinople had to import most of its grain from Egypt in late antiquity. Alexandria also could not rely on its local hinterland, collecting grain taxes from throughout Egypt and almost certainly importing a significant amount as well. A smaller city might not need to import its grain, but once we start talking about real metropoleis the story becomes very different very quickly