This is a magnificent question, except that I have no clue who you are and what your tastes are. I -- Daniel B. Holliday -- hate all spicy foods. I like things that are generally over-salted. I also have a bit of a sweet tooth . . . oh who am I kidding!? I'm obsessed with chocolate and sugar and peanut butter. I also like things on the rich side, though I do like my vegetables.
I for one would not really like the fare of ancient Rome, but by and large that which disgusts us today, disgusted them back then. That which we find tasty, they found tasty. Now, I'm not saying that the Roman penchant for offal was something we'd all like today, because it isn't . . . unless you're from a part of the world that really likes offal, then you'd get along great. So, this ends up being a subjective question. Who are you? Where do you live? What kinds of foods do you like?
Let me make a few assumptions and extend your request to only mean those foods eaten by the wealthier Romans (there were many wealthy plebeians, so we don't have to simply focus on the patricians) because that will give you access to salt, meat, and some spices from outside of the Empire. Also, let me take some liberty in excluding stuff that was plain unhealthy (like Posca sweetened with lead - yeah, yum). Also, I'm going to speak as a Westerner.
First off, you might find the food bland. The Romans did salt their food enough, but we're used to some highly engineered foods that are crafted to tickle the palate like no other food from history. After that, I say that the majority of what Romans ate on a daily basis was pretty palatable, nutritious, and you might really be surprised by how run-of-the-mill some of it was.
But the biggest thing you'd miss: Sugar. No sugar in anything. And if you're a westerner, then it's in practically everything you eat (or it's evil twin sister: corn syrup, which was also not available to the Romans). Sure, they knew of sugar (as a medicine), but they didn't know how to process and refine it. They sweetened with honey, which I dislike.
The Roman wealthy class ate a lot of fresh fruit, fish, and vegetables. If you were wealthy, there wasn't much sugar, and given the human propensity to devour sugary snacks, your basic sweets were by way of fruit or honey, so you'd miss out on Chocolate and Peanut Butter (new world stuff). In fact, a lot of the world's diet comes from the New World: green beans, tomatoes, potatoes, yams, corn, almost all gourds, bell peppers, blueberries, chocolate, peanuts, avocado, and a whole hell of a lot more. Bananas and most Citrus didn't make it from Asia until the Muslims brought them (how kind!).
But the Romans did eat quite an array of fish, meats, olives, cheeses, beans (Favas, Garbanzos, Peas, Lentils), breads, most brassica vegetables (Kale, Cabbage, Broccoli), onions, garlic, butter, turnips, parsnips, beats, radishes, cucumbers, capers, mushrooms, apples, pears, dates, grapes, pomegranates, almonds, and peaches (almonds and peaches are cousins).
In the end, I think you'd end up bored after a bit because - if you're a westerner like me with access to Indian, Italian, Japanese, Chinese, Korean, Ethiopian, Spanish, German, American, French, Slavic, Scandinavian, fast food, slow food, and grocery stores with a bazillion ingredients - the Roman table, while varied enough to keep you from gouging your eyes out, would probably not keep your interest for very long.