If accommodation is important to you, Notts has plenty of choices. Broadgate Park is just outside the gates and (from memory) accepts grad students. Albion House is a little further from the University Park campus (perhaps a 15, 20 minute walk to the law building) and accepts only grads. To make up for its distance from campus, it's only a hop, skip and a jump from Sainsbury's. Both are self-catering, but there are some reasonably priced food options on campus.
I was only an undergrad exchange student at Notts, so I can't give any real insight about the LLM programme, but I was very impressed by the standard of teaching and the facilities.