Hi there,
I attended USC for undergrad and I've lived both on and off campus. Usually grad students live off-campus, primarily because the priority for on-campus was given to undergrads. However, they're building a brand new housing building called Gateway that's opening up this fall (http://www.livegw.com/) and it's really big and nice. I'm not sure what the policy is for grad students, though.
Off-campus housing isn't hard to find, though. There's pockets of little apartment complexes surrounding USC that's within walking/biking distance, especially around the 30th St. area. Some I'd recommend from having visited/friends' experience are City Park (I lived here), The Pad, Corsica (near the Shrine), and a whole bunch of apartments along Ellendale St. If you're willing to spend a bit more money, you can look into Tuscany. If you're looking more towards downtown, Medici's great too. There's a ton of options so no need to worry
Good luck and fight on!