When arriving in Los Angeles, you will see that it is a huge city that is spread out far and wide. Determining the best area for you to live can be a daunting task, and there are certainly areas to definitely avoid.
Obviously cost will be the biggest determining factor in where you are able to live. The vast majority of filming is done in the Hollywood, Studio City, and Burbank areas. Generally speaking, the farther out from the inner city that you go, the nicer the neighborhoods are.
If you decide to live right in Hollywood, I would recommend staying away from areas south of W. Pico Blvd. and east of Western Ave. If you decide to live in the San Fernando Valley, I recommend the Encino, Sherman Oaks, Studio City, Universal City, Toluca Lake, and Burbank areas.
Another great option is just a tad northeast in the San Gabriel Valley areas of Sunland, Tujunga, and La Crescenta. It is only about 1/2 hour - 45 minutes from the studios. I lived in Tujunga for 5 years and liked it there. The rent is cheaper than most of the other areas within this distance to the studios, plus it is just outside of the rat race of the inner city. It does get a bit hot in the summer months, so I would recommend getting a place with air conditioning.
All of the areas near the beaches are great but you pay the price in rent. Anything from Malibu to Long Beach is within "striking distance" of Hollywood.
The two best free places to find LA area housing is Craigslist and Recycler: