There are alot of nice places West and South of the 405 Freeway. In Torrance, there are quite a few cool places, and as you get closer to the ocean, it gets more expensive. I would definately first get an apartment in a good area before buying anything, especially not, since prices are pretty high.
I live in the Western San Fernando Valley, about 25 miles north and west from LAX (L.A. Airport). I rarely head into Hollywood or downtown, except when needed (just went there to the Chinese Theater to watch Stan Lee put his hands and feet prints in cement).
Culver City is nice (where many of the bodybuilding events are), but it all depends what you like. The hustle and bustle with a lot of people, or less people in suburbs, etc.