The Greek diet was very healthy. They grew wheat and made breads and cereals and noodles. They grew olives and figs and grapes. They grew all kinds of vegetables. They kept goats for milk and cheese. They fished in their many waterways and streams. City-states on the coastline used boats and nets and traps to catch all kind of seafood and traded some of the catch for foods produced by the inland city-states. Some homes kept chickens. The Greeks made homemade wine. They made jams and jellies. They kept beehives for honey. They made delicious sweet deserts. They ate well.
Meals were prepared in the courtyards, the open-air center of each home. The Greeks were very clean people. Their cookers were cleaned. Their hands were clean. Their food preparation areas were clean. They did this to honor Hestia, the goddess of hearth and home.
In the larger Greek city-states, you could buy meat in cook shops. It was expensive, but available. You could also find other foods to buy in the marketplace like fancy baked goods and all kinds of fish and vegetables. But all city-states had a marketplace where foods were traded and bartered and/or purchased.