Western civilization spans Russia westward to the US and then jumps to Australia and New Zealand. It has nothing to do with living in California though, it might be argued, California is the most western civilization of western civilization.
I LOVE being in the west. I love that we have freedom of speech, freedom of religion, scientific inquiry, democracy, and tolerance (in varying degrees). Traveling to other civilizations does not bother me much, but I would never live in a non-western country permanently; even westernized countries such as Singapore, Taiwan, or Japan. I have great respect for many different civilizations but think western civilization is the flower of humanity despite all its numerous and egregious faults.
If my time machine could only take me to one place in the distant past, I'd likely choose classical Athens where my smaller penis would be considered a very sexy asset and homosexuality was the norm. Sitting in the agora listening to Plato and Socrates, attending plays by Euripides, being drinking buddys with Aristotle and Demosthenes... oh man.... Classical Athens was the cradle of western civilization and is, no doubt, why I'm so attracted to it.
The Muslims and the Chinese had great civilizations until they ossified when they turned inward on themselves. There have been other great non-western civilizatons such as Minos, Egypt, Mali, Harrapa, but they all eventually collapsed. Only western civilization has stood, even surviving a major blow with the fall of Rome and Byzantium. I think the reason is that western civilization is so adaptable and it is adaptable because the dogma of the west is that there is no dogma. We will topple ideas and theories as easily as we will topple gods.