Well, I just finished grad school here and am staying for med school as well. The grad student housing, if you can get it, is reasonably priced and reasonably nice. However, the wait-list is usually in the hundreds. I don't live there, but the people I know there got their places by being very persistent. A side note: the grad housing is not really that close to campus, it's several miles south.
UCLA has a housing website with community listings, but it's pretty weak. The best I've found is westsiderentals.com. There is a fee, but its worth it...also, if you can find someone else who already has a password then you don't need to pay🙂 In fact, I think I can get one from a co-worker if people want it.
As far as area...westwood is fairly undergrad infested and very crowded...most grad students here live in west LA, Santa Monica, Palms, or Mar Vista (the last 2 are generally less expensive). There are also several people who live a little east of campus in the hollywood/fairfax area.
I hope that helps, if there is anything else you want to know, just ask.
