LA's less a city than a motley patchwork quilt of distinct 'hoods -- one misstep, and you could either end up living in your own personal hell, or...corduroy. To find your perfect spot, check out Hubbuzz.com.
Buzz is a new apartment-rental portal with an emphasis on each locale's identity, ensuring that, even if you must move to a rat-infested wasteland, at least it'll be a "rat-friendly up-and-comer", with a nearby Ralphs. HB offers standard search parameters (price, washer/dryer, goldfish-friendly), but where it shines is with its neighborhood-specific criteria, e.g., whether you prefer Urban (Downtown), Eclectic (Silverlake), or a Hometown Vibe (Kansas). Pick a zone, and you'll get photos of the area, a Google map of nearby amenities, and a description that gets down to insider specifics; Echo Park has "an interesting architectural mix throughout, including Craftsman, Spanish and mid-century modern", while Encino's influences are apparently more...Brendan-Frazier ("What better place to put a thawed-out caveman than in the throes of an upper-middle class West Valley suburb").
Hubbuzz is free, but find an apartment through them, and once you sign a lease they'll cut you a $100 check -- with which you can buy a patchwork quilt, in case your neighborhood preference was "oceanfront windswept drafty hovel".