Safe and Affordable places to live in Los Angeles

I'm looking for an affordable (max $2000.00) pet friendly apartment in or near los Angeles. I'm a female so safety is important.
Any suggestions ?

First question is what's affordable for you? Looking for a rent of 1400$ and more in L.A and Orange county is minimum for a nice place. If you don't bother having only 4 walls around you , you may find lower rent but with other occupants ( roaches, rats and pest). Riverside county has cheaper rent but traffic to L.A is a headache! You'll need the Fastrak or Express account transponder to use the tollroads.

North Hollywood around Lankershim ("NoHo"), Sherman OaksStudio City (Studio City will be more expensive but you may find some things), Los Feliz (affordable if you find a studio, depends what you are looking for). Burbank and Glendale for sure.