I'm moving to Westwood to live with my fiance who goes to UCLA! It is a really nice, cute neighborhood with neat restaurants, movie theaters, and other stuff all in walking distance. The rent is expensive relative to neighborhoods to the south and east. It's a thirty minute drive to CSULA.
Sorry this might not be very helpful to you if you're trying to live closer to campus. But if for some reason you end up living in West LA, let me know because I'll be looking for a carpool buddy! Same to everyone else!