Central city, so no good cycling thoroughfares (surrounded by traffic, congestion, lights, etc.) close by. At least not any that I'd consider acceptable. There is however, a commuter path that opened next to the school recently that I featured in a thread earlier this year.

The good news is that there are cyclist group at USC (though I'm not sure how large or competitive they are), so group riding shouldn't be too much of an issue. The best news is the rail system next to the school which can connect you to Long Beach trails or Santa Monica (scenic) bike trails. Here's a list of featured paths.

Number 2 on the list is isolated away from traffic if you want to stretch out. But there are still some wayward dog walkers and hypnotized pedestrians (they're everywhere) you'll still have to contend with and watch out for.