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.