LA is an incredible place with loads of amazing places to stay for week or month-long intervals (lots of "creatives" running around subletting their apartment)
i can probably set you up somewhere if you want to drop a line.
i recommend venice as a beach area (also marina del rey, which is cheaper)...silver lake for an inland area that's really cool and beautiful...can't go wrong with west hollywood or the hollywood hills for sheer, um, hollyweirdness.
there's also pasadena and hoity toity areas like pacific palisades or topanga that would be fun.
keep in mind that LA is freaking HUGE (roughly 30miles by 30 miles).
and also that it's optimal to be here october-april (although the beach areas are temperate year round...it can get hot once you're >10 miles inland in the summer).
The people in Orange County are basically how they are portrayed on MTV, but Laguna Beach is really beautiful and has great beaches. You could probably find a spot there in the off-season that you'd love.
I found this service to be pretty useful for finding apartments in specific areas:
kexter.com
holler if you'd like some help!
ethanbauley // gmail
(Virginia transplant)
(PS you really need to post up in Big Sur or somewhere similar on the north side of SF. Sonoma/Napa is incredible, too).
Just saw your budget, you will be set up with INCREDIBLE studio/1 bedroom places in LA w/ that budget. You could do it for less.
I might think about losing the pickup truck for this trip...but I'd have to crunch the numbers ;-)