Any particular area in LA?
If you don't want the horrible commute then I would suggest you narrow your area a bit further. But if you are starting out keep your options open and decide once you have an offer:
A) El Segundo/Santa Monica area. Mattel, Belkin, Pip, Stuart Karten, Ashcraft Design, T2 Design, Pulse Design, Tandem Design and a few others.
B) Irvine - Vizio, Lum Design, Bosch/Thermador, Simplehuman, Footwear/lifestyle companies, Aspen Medical Products, Other Medical Companies, and a few other corporate firms.
C) Burbank area - Disney, Munchkin, ID by M, and others
D) RKS and Designworks are in the Newburry Park/Thousand Oaks area...northwest from LA
E) Long Beach/Lakewood/Huntington Beach - ID Group, Nectar Product Development, GK International, Zodiac Aerospace, OlloClip, SitOnit,
F) Chino Hills/Corona Area - Jacuzzi Group (i believe they currently have a posting for a JR Designer).
There are a lot of options but I would agree is not an overwhelming number of job postings. Are you looking for corporate or consulting? Toys, Medical, Electronics, Lifestyle, Furniture?