I know they ate VERY healthy, and a Mediterranean diet is proven to be the healthiest of all.
I want to model my diet after them in that time. So far I believe they ate:
Yogurt
Grapes
Lamb
Olives
Tomatoes
Milk
WHAT ELSE IS THERE?!?!
olives [especially olive oil was used and eaten with everything]
figs
cheese
breads [barley & wheat]
fish
eggs [chicken and quail]
raisins
pomegranates
honey
seafood [oysters, lobster, mussels, squid, octopus]
onions
lentils
peas [garden, sweet, chick, etc.]
venison [including wild birds and hares]
cabbage
nuts
poultry [chicken, goose, duck, quail]
pork [especially sausages made from pork meat]
spices used - cumin, coriander, oregano, dill, parsley, mint, pine cones, fennel, aniseed, poppy seed, garlic
beef, goat & lamb - was expensive and the poorer populace only ate it on festival days. Fish, seafood, poultry and wild game were their main sources of protein.
milk [goat, ewe, cow] - was very rarely drunk, it was considered barbaric and milk was used for making cheese. Pyriatē was a thick rather sour milk that was drunk and is today commonly mistaken for yogurt.
wine - was drunk every day, even with breakfast. It was however always watered, drinking it "straight" like we do today, was considered barbaric by the Greeks [or Hellenes as Herodotus called them].
tomatoes - were not eaten in ancient Greece, since they didn’t have them. Tomatoes originally came from South America and were introduced to Europe by either Columbus and/or Cortés during the 1500’s.
You should look into the Turkish and Italian diets as well if you want a fuller range of Mediterranean cooking. It is healthy and delicious! You could also check on the Spanish and Algerian diets.
Edit: also remember that the modern Mediterranean Diet and the ancient Greco-Roman diets differ considerably. There are many more foodstuffs [such as tomatoes] available and used in Mediterranean cooking today.