Tea, that's totally awesome! Rome is a really neat city.
As for Greece, well, let it be noted that many of the ruins and elements that one might see in Greece are the result of the Roman occupation, or at least buildings constructed under the Roman overlordship of Greece. So, for example, we get the theatre in Athens - not, of course, the Classical one, but rather that built by Atticus. Also note... it just says 'a trip to Greece', so it's not exactly like one's going there to study. And anyway, KebreI, the same thing might be asked of Rome, as they don't speak Latin there, either. It's to get a sense of the ancient peoples who spoke this language - and to see the Pantheon, and to walk the ruins of the Forum, does aid in that.
However, tea, I would disagree with you on two accounts. I do not think they spoke Greek amongst themselves (even their written correspondance was typically Latin), and there are very few Greek words in Latin.
All the same, that sounds like a wonderful opportunity that you should most certainly sieze with full-hearted zeal.
