Gege,
All joking aside, please don't be put off by this talk of violence. We're not talking about downtown Baghdad here. Neither Derby or Nottingham are any worse than any other metropolitan area, and certainly more safe than London (last Thursdays atrocities aside) where your Cousin lives. Every city has 'bad' areas where you would avoid going.
Nottingham is a vibrant, cosmopolitan place with a wide and varied nightlife. With a young population, due to the two Universities and numerous colleges. I've lived in the area for over 30 years, I've moved out of the area and then come back again if that's any indication. I'm not a native, but I choose to live in this region. The cost of living is reasonable in comparison with the S.E. of England for example, and the people are friendlier.
It is centrally placed so you can get to anywhere in the country reasonably quickly, London will take an 1½ hours on the train and two hours by car.
Hope that helps