Very similar to modern cuisine in Italy and the Mediterranean\Middle East with the exception of ingredients like tomatoes, spinach, eggplant, and red peppers.

As a Roman governor you might enjoy a light breakfast consisting of flatbread(called emmer and made of wheat) perhaps with cheese, eggs, fruit, honey, milk, olives, and you may dip the bread in wine.

In the afternoon around 2pm you would have cena, sort of a lunch\dinner, that may last late into the night (particularly if you were entertaining guests).

There would be two courses: a main course and a dessert one. The main course would feature puls (similar to porridge an made of wheat with perhaps water, salt and fat but if you were eating fancy which I assume, it would include olive oil and various vegetables). The puls would be eaten with eggs, cheese, and honey, and sometimes with fish (a wide variety to choose from here including tuna, mullet, sea-bass, and shellfish like oysters and even snails) or meat, usually grilled or roasted (wild boar, venison, pork, lamb, beef, various sausages\smoked meats, poultry). Game meats would be a cheaper and more plentiful option than the butcher's meat which was eaten mainly by the upper classes and on special occassions, however.

Dessert would consist of fruits (apples, pears, grapes, various berries, dates, pomegranates, lemons, citrons, and melons) and shellfish (oysters, molluscs, shrimps, snails) and afterwards might come a round of alcoholic drinks (comissatio)

When it comes to delicacies stuffed dormice (yes the little rodents) would be quite a treat, packed with cheese, herbs and other tasty additives. Gamut (an extremely salty sauce made of fish, that tasted something similar to Worcestershire or soy sauce) would be used to season many dishes (kinda like sriracha today :-D)

There is a recipe called "Placenta Cake", made of layers of cheese and a king pasta-like flatbread, baled and the covered in honey. Apparently, Cato the Elder enjoyed this, as he wrote a surviving recipe for it.

When it came time to drink, wine would be the most popular and liked option, and was mixed with water to a drinkable dilution (it was very strong straight-up and not consumed this way). It could also be flavoured with raisins, honey, pepper, dates, saffron, or laurel. There is one variety made with resin that was said to be an acquired taste (I bet). Beer would have been known, but would be considered a vulgar drink for barbarians (Egyptians were very fond of it, as well as Persians and Germans).

You also would have a nice selection of veggies, herbs and spices making your meals quite colourful. Garlic, olives, cabbage, lettuce, broccoli, onions, sesame seeds, carrots, beets, radishes, cucumbers, green beans, kale, leeks, proto-sweet peas and flower varieties to add flavor and colour.

You might find hazelnuts, pine nuts, walnuts and almonds in your plate, as well as lots of legumes: chickpeas, lentils, fava beans, and peas.

Sources:

Natural History by Pliny

Georgics by Virgil

The Oxford Encyclopedia of Ancient Greece and Rome

Livy

Suetonius

The Culture of Food by Massimo Montanari