I agree with emoley's here: it's a pretty rough commute. If you want to live in an area that a little more artsy with events going on you can try Venice--being by the beach though, it isn't cheap. A lot of students are in Palms/Culver City, which puts you somewhat between UCLA and Venice. If you do try to commute from somewhere farther, be sure to figure parking into your budget. When I have to get on campus and drive it's $9/day for a full day pass in the on-campus lots ($6 for 2 hrs, $4 for 1 hr, I think). At $45/wk if you commute every day, I'd look into living somewhere with a bus route. As a note, you won't really be able to park you car down in Westwood or anything. It's all metered.
Good luck with the housing search.