I want to add a more positive review of Broomhall! I don't live as far down as William St/Exeter Dr which have been commented on previously, and I admit that particular area seems a bit less desirable/safe.
However, I have lived in Broomhall for 6 years and have never experienced any problems. I live near Broomspring Lane and I feel safe walking here at night (actually feel more safe here than previous areas I have lived in Sheffield). My particular road is very quiet and there have been no obvious signs of trouble or disharmony.
As stated in the original post, location wise it's great, especially if you don't own a car. Five minutes walk to town or to the nearest tram stop, very near to Crookes and Ecclesall Road etc.
It sounds like some people have had some genuinely bad experiences in this area, but just wanted to say that I personally haven't and enjoy living here