What it feels like as a PhD student in math or computer science in the US I am currently an undergraduate in Canada, but I am interested in math/comp sci PhD in the US. I heard that an academically supporting environment(the environment of the school? of the department?) in PhD study is very important. Also, I heard in some schools, PhD students don't like helping each other, because they think they are competing, which is a sign of bad experience. In some other cases, the adviser might be unhelpful or even selfish. So how can we choose a university/department/adviser to ensure a good study experience? If you are a PhD student, do you like your department? I like any personal experience or examples.
This is not really an answer but a (somewhat) relevant anecdote that's too long for a comment. About 20 years ago, I chaired my department's graduate admissions committee. The college had a requirement that new graduate students whose undergrad degree is from outside the U.S. must participate in an orientation before the start of their first semester of enrollment, to acquaint them with various aspects of life in the U.S. and, in particular, university life in the U.S. We could apply to an assistant dean to have specific students exempted from this requirement. We had admitted a student who did his undergrad work at the University of Waterloo (Ontario, not Belgium), and I requested that he be exempted form this orientation requirement.

I thought (and I still think) this was a no-brainer, but the assistant dean wanted evidence, meaning information from people who had taught at the University of Waterloo. So I had to write (with some embarrassment) to a few of this student's instructors, asking them for the necessary information about similarities and differences between Waterloo and Ann Arbor.

One of the responses ended with a sentence that, I think, summarized the situation very well: The only thing the student will have to get used to in the U.S. is the absence of Tim Horton's.

End of anecdote. 

We now have Tim Horton's in the U.S. So I suggest you think about U.S. universities the same way you'd think about Canadian ones.