I live in a 'nice neighbourhood'; I don't have to be that careful do I?
I think it's important that wherever you live, even if it's a nice neighbourhood, you maintain a sensible balance between not being too afraid of crime, but not being too complacent, either. You should travel around wherever you live taking a sensible precaution, showing an awareness of where you are. Don't leave your personal property openly on display so that it becomes a potential invitation for someone to try to take it from you. It's important to be safe and sensible, no matter where you are. However, you should also not be too overly afraid of where you are.