How much the region you get your PhD is important to your career path? I am about to make an important decision for my career. I have a good PhD position (fully funded with a good stipend) in East Asia. The university is one of the top 50 in my subject, which is electrical engineering and computer science (based on QS, THE) and Top 100 generally (QS, THE). The professor is somehow well-known and has an established international connection: He graduated from a top US university and is the author of a well-known book on the subject, associate editor of prestigious journal, etc.

I want to say everything is good. However, I ultimately seek a position in the West and not the East. At the moment I’ve missed the opportunity for Western schools for Fall 2018, and such an opportunity might not be offered to me in Western universities.  

Here is my question: Assuming that I manage to produce good research and a good CV with a good international collaboration, does having a PhD from abroad (esp. East Asia) dramatically lower my chance of a research career in the target country (let's assume the US, but I am asking more generally)?

I want to compare the importance of individual merit for career and the region you get your PhD. What’s its impact?
It's difficult to answer your question with too few details.

You can look at the alumni of the lab/department that gives you the offer. What were their first jobs after leaving the lab? If none of them went to the west, then it is very unlikely that you will do :)

East Asia is very broad, which includes China, Japan, Korea etc... There are only a small set of universities that are known to the west. These are the one or two top universities in the most developed countries in the region, e.g. NUS in Singapore, KAIST and SNU in Korea, Todai in Japan, etc

If you obtain a PhD from a university outside this list, it will be significantly difficult for you to find a position in the west after PhD.

Theoretically, if you have a strong publication records, LoRs from big shots in the fields, you can get a good a position after PhD. But in reality, it is easier to achieve that (papers, LoRs etc) if you are in a top university.