Honestly, I have no idea why you want to move to L.A. I was happy to get out of L.A. and most of my friends have also moved away. The ones left in L.A. are planning to move out. Housing costs are ridiculous. $120K to $140K isn't going to go very far.
In addition, to the insane housing costs, L.A. also has horrible, horrible traffic. And unlike NYC, L.A. lacks good public transportation. So almost everyone has to drive. Housing is most expensive near the coast and in desirable areas like Westwood, etc. Typically, the farther from the coast one goes, the less the housing cost. Therefore, it is very common for people to commute long distances, for example from Riverside or the San Fernando Valley into the West side of the L.A. area. Many Angelenos spend 2 to 3 hours or more every work day sitting in a car in bumper to bumper traffic. Not only that, there is no "rush hour" anymore - rush hour is almost 24 hours a day.
San Diego is more affordable, but prices are skyrocketing there, too. If you want to live in California, consider some of the inland areas and smaller towns and cities. You will make the same, or more money, than in LA and the cost of living will be less than half as much. I just got a job offer for the Nevada side of Lake Tahoe for $120K and I am a new grad NP. Nevada also has no state income tax, very low property taxes, and a lower sales tax than California, yet I am within a 1 hour drive of California, not to mention being near beautiful Lake Tahoe and within a 30 minute drive of Carson City and Reno, 2 hours to Sacramento, 3 hours to San Francisco. There are many beautiful towns in Northeast California that are similar - Placerville, Oroville, Redding, etc. These cities are all within an easy drive of Sacramento and San Francisco. While people often sneer at places like Fresno, these are big cities with a high need for providers, a low cost of living, surprisingly nice, and an easy drive to both L.A. and San Francisco, as well as the Sierra Nevada mountains.