The Western suburbs span a very large area of Melbourne. Historically, it has been considered the poorer, working-class side of the city. But more recently, there has been huge development and a notable improvement in the socio-economics of the area.
Although all of Melbourne is an extremely safe city, the Western suburbs have a local reputation of having a much higher crime rate than the east or north. You should be careful of your belongings, and avoid travel during the night. There should be no issues during the day. The larger suburbs of Footscray and Sunshine seem to be the most notorious.