My understanding is that a lot of how they look at the world has been tempered and governed by a history in which they were invaded numerous times from all sides. They don't see themselves as either "Eastern" or "Western," but they've had to deal with enemies from both sides.
When I've talked to Russians, they seemed very interested in America. I think that they respected us, and I think they liked some aspects of America and American culture. But they also saw us as somewhat misguided, greedy, immature, and hypocritical in a lot of ways. I don't think they truly hate us or disrespect us in any real way, but they are aware of our faults and weaknesses in a more perceptive way than most Americans are able to.
They may also see us as somewhat "wild" and unpredictable, so they might feel the need to play the hard line because they're not really sure what we're going to do next.
Some of the schism between Russia and the West has long-term historical origins due to the schism between the Eastern and Western Church. And then, during the Soviet period, the Russians were viewed as atheists, but they actually do have long historical traditions of being devoutly religious and spiritually-led. That seems to be more the case nowadays, too, since the fall of Communism.