I live in Los Angeles.
When are you planning to come out. Right now Mount Gorgonio and Mount San Jacinto all have snow and are about an hour drive from USC area. San Jacinto has tram that will take you up the first 8000 feet and then it's a short 5 miles to the top, well worth doing.
Lots of big trees and mountain air.
If you want to hike up to Mount Gorgonio (old greyback) then take the trail to dry lake, it's another 5 mile trip.
If you want to walk along the ocean there is a bike path from Santa Monica pier to
torrance 26 miles
The USC neighborhood is safe on campus, a stone's throw from the campus is a rougher neighberhood, not a place to get shot but car thieves and prostitues much like every big city in the country but generally Ca is a gentler place than most of the country.