Ask realtors for recommendations, search neighborhoods online for crime statistics, or you could even call the city police departments for more information.
You can always check the crime rates online or read up on the different neighborhoods online. You can also find realators that will work with renters that can help you find the right place.
Look in the local news paper. Make sure the apartment is in a safe area, you can usually tell this by driving through the area and examining the people/building condition.
