I have been accepted into LLM programs in International Law at the University of Westminster, University of Buckingham & University of Sheffield.

I know these are not top tier schools but I am not a top tier student; thus my options were slightly limited. I was wondering if anyone out there has any experience or an opinion on the quality of the LLM programs at these schools.

Also, I am from the US and lived in London years ago but never been to Sheffield or Buckingham so I am interested to know what the lifestyle is like in the other cities.

Thanks!

Sheffield is one of the old universities. It has had its ups and downs over the last decade but has had consistently a good reputation with undergraduates; the university/city has one of the highest rates of graduates staying on there to live in the UK - that from someone who worked I think for the council there and some time ago, but probably not far off. In research terms it did comparatively well in the last RAE - especially given it had lost a lot of staff; I'd check staff-student ratios and whose teaching, but some good people have worked there.
Westminster is a former poly but one which seems to be making serious efforts to act like an old university; A lot of work has gone in to developing the post-grad programme, and also a research profile (its performance from memory was not as good as Sheffield which ever way you try to calculate the numbers). In terms of old polytechnics, one of the best (possibly outstripping places like Nottingham Trent). From the perspective of an undergraduate there would be no competition between it and Sheffield - old over new, every time. I'm not sure if the same holds true at post-grad level or not. It may depend on what you are interested in - for example bioethics, sheffield; media Westminster (though of course there are other institutions with strengths in both these areas) - neither leap to mind particularly for international law, but then I haven't checked the staff listings recently so I could be wrong on that. Obviously Westminster is in London so has all the strengths and weaknesses that go with that.
Buckingham I know nothing about; I don't even know if people there do research and I would have thought that at p-g level you would want research active staff.