If I could expand the list of candidate civilizations, I would choose the Sumerian civilization from about 5000 BC. Often termed as the first true civilization in human history, most of their innovations from agriculture, to urban development, to the fields of science, mathematics, the art of music, sculpture, painting and even writing, all would have had their basic formation in the way we now them today with them.

If I had to choose between the Greek or the Egyptian civilizations I would probably choose Egypt when it was under Greek rule and Hellenistic influence, during the period right after the founding of the Ptolemaic dynasty by Alexander the Great, roughly from 320 BC to 20 BC. ( some might see this as a cop out answer, LOL, as I am selecting a hybrid Greek-Egyptian period)

These would of had been the days when the city of Alexandria became the center of knowledge for the ancient world. Being able to see the great library of Alexandria, the light house; that would be most exciting.

That is a hard question. I love both areas and both of their ancient days intrigue me. I think I would go with Greece, it seems that their location was a little more comfortable with less sand and more trees and vegetation.
So I think Greece would be my choice.

I don't think it would matter as not being from that Country we would all be slaves there.