Answer: A. Greek ideas of citizenship and democracy remain some of our most cherished values.
The sunny peninsula in Southern Europe surrounded by the Mediterranean that the sentence refers to is the Greek peninsula, and the principles and ideas are those of democracy and citizenship developed by Ancient Greek philosophers. The passage argues that these ideas "still shape our modern world," which means that, nowadays, these remain some of our most cherished values.
Eudemonia is best described as "The good composed of all goods; an ability which suffices for living well". It means happiness or welfare but if translated, it's meaning is "human fluorishing".