Best of the worst neighborhoods nearest Westwood/UCLA

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My youngest is transferring to UCLA in the fall.  Our kid's friends who have attended  usually rented in Westwood. But their parent's were willing to spend way more money than I probably am.  I mean like WAY more.  I'd buy something before I'd spend that kind of money on a college rental in So Cal. Also, my daughter doesn't desire to be on or have a need to be that near campus.  

I like Echo Park and Silver Lake but those are pretty distant when considering traffic.  For those of you in the LA area, what's the closest worst neighborhoods you would consider buying in if it were your daughter? It doesn't have to be the worst neighborhood, of course. Just the cheapest.  :)