born and raised in Long Beach, went to school in LA—-> because they are driving cities even the most dangerous neighborhoods don’t feel as dangerous because you’re in a nice little bubble.
long beach is cheaper but less convenient—> belmont shore is crazy safe and has lots of socal sororityish blondes and surfers who go to cal state and hang out at the bars on second street. the art district downtown is less “safe” but not really dangerous (my grandmother has been living there since way before it was gentrified and she’s never had a problem), cheaper, much more hipster, cafe, gallery, music vibe. avoid the heart of downtown and super north long beach (ie – compton) and you’re beyond fine.
LA—> culver city is cheapish and way trendy, then santa monica, lower hollywood hills, and 3rd + Fairfax/La Brea are pricier but way young and safe.
wouldn’t worry too much about safety – maybe it’s a familiarity thing, but i’m currently in new york and even the nicest neighborhoods feel more dangerous than the skeeviest of the southern california.
in terms of living in los angeles and being happy, commute is more of an issue than safety.
i’d find a place that’s walking distance to your job – get a bike – then soak up the winter sun, mexican fruit stands, strip mall sushi, and infinite possibilities. cheers!