Firstly, the Bible makes a good source on this. However, it's only a secondary source, and that's always best backed up with primary evidence. To that end, I present archaeological evidence from Near Eastern Archaeology.

Onto the good stuff then.

Contextually, this period in history was a heavily religious time, and ritual was important in this regard, especially with the varying subgroups in religions(I think the appropriate term is cult, but not in the modern meaning). Food was thus divided into two groups - that which was regularly consumed, and that which was consumed in keeping with the cultic practices.

Also important is the idea of food as a cultural concept, which functioned as an identifier of a person's cultural group - especially in a time without strictly defined borders.

With these two points in mind, we can make a list of what was available, and then look at the dietary restrictions of Judaism.

Grain

• Was often eaten fresh or roasted.
• Made into breads and stews/gruels, both of which were healthy options.

Meat

• Meat was not a daily meal for the regular person, but most likely a once weekly food.
• Domesticated cattle: Sheep, goats, cows
• Seafood
• Poultry: Chickens, ducks, geese
• Food that was hunted,

Dairy

• To deal with the hot temperature of the Middle East, milk was often turned into other products as well as being consumed as a drink. *Cheese, butter, yogurt were all common, especially with domestic herds at hand.

Fruit

• Figs, pomegranates, grapes, apricots, dates, apples, olives
• Berries such as blackberry and black mulberry

Vegetables

• This category is prefaced by the statement "An important food group that is not well known from the written and archaeological records.
• Carrots, cucumbers, musk, watermelon, onion, garlic, dandelion, capers.

Miscellaneous

• Honey as a sweetener
• Olive oil
• Grasshoppers and locusts
• Seasoning such as salt and herbs
• Vinegar

The festive occasions are described "as the entertaining of guests or civic and cultic festival". These events would almost certainly have featured meat, with certain cuts being reserved as the best parts of the animal for the guest.

Nobles ate in finer style than the common folk, as might be expected. Sinuhe, who lived several(read: 19 or so) centuries before Jesus was an Egyptian nobleman who ate bread, meat(both domesticated and desert animals that were hunted) daily, as well as wine.

A final point: obviously not everyone would be able to hunt, or fish, and to this end there were markets where these items were readily available for purchase.

Source:

'Eat, Drink and Be Merry: The Mediterranean Diet', Near Eastern Archaeology, 2004, by Oded Borowski.

Obviously we will never know what food Jesus ate, but we can take an educated guess on it by assuming that his diet was similar to other Jew's in the area and time period.

These are some foods that Jesus is likely to have consumed:

Olives Figs Grapes Lamb Legumes Melons Pomegranates Dates Nuts Raisons Milk Cheese Eggs Cucumbers Fish Bread Corn Wheat Honey Wine

Basically the average food of an early 1st century Jew.