There really is no limit to the things that can be seen or done in SoCal. It would depend on your tastes, energy, and finances. Time is another issue, but that is closely related to finances. I lived out there for six months and we would ride our Harleys in the canyons and then drink beer and eat oysters at Gladstones in Pacific Palisades. It was a cheap way to have fun and incorporated a lot of the things that people think of when they think of LA. Of course, I was 22 at the time, so my tastes have changed. We also used to hit Joe Jost's in Long Beach for beer and pickled eggs.
You can surf, ski, hit the tourist stuff in H'wood, shop in Beverly Hills and see if there are any werewolves in Trader Vic's...There are no more "Payday Wednesdays" at the LAPD Academy, so that one is out...
As for the immediate vacinity around USC, it's not exactly a tourist Mecca.