I lived on the Narb for years. One of my best mates still lives up towards Braunstone Town. Never once did I have any issues with anyone in that area, even during my more hedonistic days. Maybe I just got lucky.
There's plenty of dodgy people around, but there is in every town and city. The country is fvcked. It's no surprise.
Closest I ever got to getting in trouble was when some shirtless junkie (who was very much a Leicester local, by the way) chased me around Castle Park Benny Hill-style because I refused to give him a quid.
Brauny Gate and the area towards the university is so much better than it used to be.