We see this every day in this forum: Everyone wants to move here, and is looking for “cheap/affordable and safe". However, such a place just doesn’t exist; the two terms are mutually exclusive. It's all about supply and demand: If it's in SoCal, then it's not going to be cheap to begin with. If it's a safe area, then it's more expensive. If you need good schools, add a couple hundred bucks a month on top of it.
If you want to live here and enjoy the weather, then you have to pay for it. You put up with the smog and the traffic, enjoy the weather and pay your rent or mortgage. My advice is to start checking out craigslist, rent.com, and apartments.com if you are looking to rent. You’ll quickly see that the minimum rent for a non-war zone is about $1,000-$1,200 per month for a studio or 1BR. Really nice areas (like the West LA area) easily run $3,000 or more. Want to live near the beach? Expect to pay a premium.
"LA" is such a big place, there are so many neighborhoods/cities where you can live. Of course, even within a city or neighborhood, there are safer sections and less-safe sections.
In Los Angeles, some nice sections are West LA, Brentwood, Westwood, Marina Del Rey, Playa Del Rey, Los Feliz, Silverlake, Eagle Rock, Encino, Tarzana, Studio City, Toluca Lake, Granada Hills, Woodland Hills, Sherman Oaks, West Hills, Chatsworth.
To the east: South Pasadena, parts of Pasadena, Altadena, Arcadia, Monrovia, Glendora, San Dimas, Laverne, Azusa, Rancho Cucamonga.
Along the beach: Santa Monica, Marina Del Rey, Playa Del Rey, Redondo Beach, Manhattan Beach, Hermosa Beach, Torrance, Palos Verdes, Rancho PV.
In Orange County aka "The OC": Seal Beach , Huntington Beach , Newport Beach , Corona Del Mar , Laguna Beach , Dana Point , Capistrano Beach , San Clemente , Brea, Yorba Linda, Orange, Tustin, Irvine, Laguna Hills, Rancho Santa Margarita, Lake Forest
To the west: Agoura, Calabasas, Thousand Oaks, Westlake Village, Simi Valley, Moorpark.
This is not an all-inclusive list, but it's a start.