UCLA is not located in the dangerous part of Los Angeles. It is bordered by Beverly Hills, Bel Air, and Brentwood. You are probably thinking of USC (which is Downtown).
Also, while the state of California as a whole is suffering economically, UCLA and Berkeley are doing quite well.
I believe that the stipend for students in the Indo-European program is around $23,000 a year. Certainly enough to afford a decent place in Culver, Brentwood, or Westwood.
Just thought I'd offer my two cents.