dailybruin.ucla.edu---look for the classified section
losangeles.craigslist.org---search for Westwood in apartment rentals
cho.ucla.edu---enter your UID and search for either sublets or apartments for rent
These three, and westsiderentals, seem to be the big sites. If you are close enough to campus, you should definately go there and simply walk around Westwood and up and down Hilgard and call up every apartment complex (there are banners on each building) that you pass to see if there are vacancies.