I apologize as not many people offered help. Near Los Angeles, areas that would be cheap, nice, closer to the city I would say look into the San Fernando and San Gabriel Valleys. San Fernando has Burbank, Glendale, North Hollywood, Studio City, etc. San Gabriel Valley has South Pasadena, La Canada Flintridge, Arcadia, Glendora, Monrovia, Walnut, San Dimas, Diamond Bar, etc. Closer to LA, and you get to gentrified areas and older areas--Silver Lake, Eagle Rock, Echo Park, Los Feliz, West Hills, Holmby Hills, etc.
Anywhere closer to the ocean gets more expensive. You can give it a shot in Torrance, Santa Monica, parts of Long Beach, etc.
West LA is also expensive but nicer--Brentwood, West Hollywood, Westwood, Santa Monica, etc.
North LA is a mix between the San Fernando Valley and more affluent coastal areas--which tend to be more expensive.
There is also Orange County--though be prepared for a commute and more expensive housing on average. Orange County is next to LA County however. Try Brea, Huntington Beach, Irvine, Fullerton, Tustin, Anaheim Hills, Placentia, Costa Mesa, etc.
You can also try Ventura County (Moorpark, Simi Valley, Ventura, Valencia, Thousand Oaks) which is a bit farther away north and also somewhat expensive.
If you really don't mind a commute, you can try MUCH cheaper but very nice options in Riverside County (Corona, city of Riverside, Temecula, Murrieta, etc.) or San Bernardino County (Rancho Cucamonga, Claremont, Fontana, Upland, Chino Hills, Redlands, Yucaipa, etc.).
Aside from Los Angeles and San Francisco, there is also Sacramento in northern California not too far from San Francisco, and San Diego in southern California not too far from Los Angeles. Of all 4 major cities I would pick San Diego, because it has the best weather, is right by the beach, compact, lower cost of living/less expensive, cleaner, and is not too far from Los Angeles. If you would rather go with an area closer to Los Angeles, I would pick among some of the areas mentioned above.
One last note: Downtown LA is gentrifying as well--though it is also becoming pricey.