This question is really a matter of opinion since it is not really possible to A) say for certain how westward expansion affected our culture or B) to say whether any impacts that we can identify were good or bad. However, we can at least speculate as to how westward expansion affected us and we can try to define those impacts as good or bad. Let us look at two impacts of westward expansion and try to say that they have had negative effects on our culture.
One of these impacts would be the idea of manifest destiny. Our expansion (arguably) helped to give us the feeling that we were better than other people and that we deserved to expand at their expense. We can argue that this feeling made us arrogant and has poisoned the ways in which we interact with other nations.
A second impact would be the way in which westward expansion gave us a feeling of independence and self-sufficiency, at least in our collective memory of this process. We believe that our westward expansion was carried out by rugged individuals who could take care of themselves and had no need for governments or other such things. We can argue that this continues to hurt us today. We can argue that it makes us less likely to feel compassion towards people who need help. This makes us more likely to oppose government programs to help them. We can argue that this feeling makes us more likely to want to own guns to protect ourselves. We can argue that this leads to more gun violence.
In these ways, we can say that westward expansion had negative impacts on our culture. However, there is no way to prove that it had these impacts or to objectively say that they were negative.