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I am an EU citizen who is going to apply to PhD Physics programs soon. My ultimate goal is to become a university professor. In considering which university I should attend for PhD, factors such as tuition & program differences don't matter to me. What matters is that I don't feel like doing (nor do I agree with) the GRE (which would require a significant preparation), thus applying to PhD programs in the US might be out of the picture for me. However, the question pertains that if I want an academic career (ultimately, a professor position) in the US in the future, does it matter from which university I get my PhD degree?
Note: I do not care about a uni's rank or status. What I care about is whether the uni's location (different country) will affect where I can get jobs later on...
PS: On a separate matter, I've heard that PhD graduates in the US can obtain academic jobs without going through postdocs, is that true? If so, what does it take do achieve that?