UCLA is located in West Los Angeles/Holmby Hills. There are quite a few apartments to the west of campus on the other side of fraternity row, but the competition is fierce for these because of their proximity campus. If you don't mind either driving or taking public transit, there are numerous areas west of the 405 Freeway in West Los Angeles, Santa Monica, and Venice. Culver City is also a good option; being almost due south of campus and more affordable. Seek and ye shall find. Good luck!