I don't know much about Edinburgh or Cardiff, but I can tell you all about Leeds!
As far as I can gather Leeds has a good reputation for Business, and has a relatively new Business School (its all shiny and new and looks like a church!) I think the languages department is quite good as well but I've only heard that from my friends studying languages!
The majority of the student housing is in Headingley and Hyde Park, about 20 minutes walk from uni, although a couple of the first year halls of residence are about 5 miles away from campus. Quite a lot of the more recent first year complexes are en-suite now and are full kitted out for internet access (if your prepared to pay for it obviously)
The city itself is supposed to be one of the fastest growing in Europe, which has its good points and its bad points, ie, fantastic night life and shopping but some areas are practically slums and it can be a bit intimidating when you first arrive.
If I can be of anymore help, PM me. x.