I'll be completing a BS in Computer Science at the end of next year and am unsure about graduate school. I study at a fairly lowly ranked school for this field with somewhat mediocre performance and as such I am planning to pursue a Masters degree before applying to PhD programs. I'm in my university's 5 year BS/MS program, but I was curious if I might be better off applying to an MS somewhere more well regarded. The main advantage of the combined degree seems to be convenience as well as a smooth transition to research (I'm aware of the faculty at my school and generally what they work on), but I'm curious about the degree to which my choice of MS might affect PhD admissions.
Yes, preferably go somewhere else for the M.S. if what you want is the M.S. degree. The benefits of 'new challenges' (already mentioned) are worth it.
However, if your goal is to be admitted for PhD, then the research experience that you could get ahead of applying for PhD will be more valuable than the M.S. degree. I've seen PhD applicants with stronger research experience and having BS degree only, than other applicants that have a MS. If you can start having conversations with faculty at your institution with whom you'd like to do research, then you'll be able to make a better decision. Just be clear with them saying that you want learn and do research to have a better chance for PhD admission at other schools two years down the line.