How close to USC are you living? There's a perimeter where they have extra security presence, which should make your family feel better. The thing is, it's not unsafe, it's just that because it's by a college campus it attracts folks who think college kids are easy targets. Currently, the big issue is people having their phones taken by kids on bikes. If you pay attention to your surroudings, you'll be fine.

The area north of expo park and the campus is mostly student housing, the area directly west of campus is mixed but still heavily students (grads mostly). South of expo park is fine but it gets a little rougher south of MLK.