There are two quantum wikis which provide reasonably good list of research groups in QIP: Quantiki and Qwiki. Quantiki has better European coverage, while Qwiki has better US coverage.
The geographic area I know best is the UK. In the UK there are large theory groups in Oxford, Cambridge, Bristol, University College London and Imperial College, among other places.
In Oxford, where I have spent the last 5 years, QIP research is spread across a number of departments: Physics, Computer Science, Materials Science and Maths. There isn't much of a presence in Maths, although it is Artur Ekert's official affiliation. Computer Science has a growing group that mostly looks at category theory and quantum foundations. Physics has quite a number of different groups ranging from experiments to theory. Materials science is weirdly the department where I have been based (although I know little about materials) and there is both a theory group there and a fair number of experimentalists. Computer Science, Materials and Physics all have taught quantum computing courses which can be taken towards the course requirement of a DPhil.
Hope this is useful.