Adjacent farmlands
Food supply for the Italian city-states of the late middle ages and Renaissance largely came from their own adjacent regions of land, known as their 'contado'. Much of the land in the contado tended to be owned by inhabitants of the mother-city but countryside-based landowners also existed. As city-states grew, however, their contados often became inadequate for their food needs and therefore required mass imports of foodstuffs to maintain their existence.
Given Italy's diverse geography, the arrangement between one city-state and its contado was never uniform but the basic system used in many of the northern Italian city-states was known as 'mezzadria'. Here, the urban landowner provided the land, housing and equipment for the tenant's family, or 'mezzadri', to grow crops. A contract was agreed annually or every several years where it was decided what proportion of crops would be sent to the city and how much would be kept by the tenant. These arrangements were either exploitative to peasants or fairly balanced, depending on the city-state. The city-state of Lucca, for example, where much of its contado was mountainous, tenants in more fertile areas of the contado were pushed harder to produce. In Perugia's contado, on the other hand, with it more fertile land and relatively small-population, contracts appear to have been fairer.
Although a contado would produce much of the food for its city-state, the rapidly expanding city-states soon outstripped supply and had to look elsewhere for food. Despite being situated in highly fertile in the Po Valley, the city-state of Florence could not rely on its own contado for even half of its food needs by the mid-14th century. The sparsely populated Mezzogiorno in southern Italy therefore served as Florence's breadbasket, in exchange for large loans. The economic prosperity in northern Italy meant that if a city-state could not provide for itself then it could pay for somewhere else to help provide for it.
Thanks for your response, that really gives me a much clearer picture of the organization of supply to large Italian cities in that period. I'm still very curious about the German ones as well where circumstances might have been very different