My favorite stores have all been mentioned, but as to my favorite eats/drinks:
Food:
Sona (One of the few LA eateries I'd consider world-class, and about as unpretntious as they come)
Comme Ca (Not the most authentic bistro, but always great food and a great atmosphere)
Le Petit Greek (on a really nice, out of the way street in Hancock Park, pretty good traditional Greek fare)
Lucques (Can't exactly classify the cuisine, but very, very good)
Boa (Others will prefer Cut or Mastros for steaks, but I prefer the SM location of BOA)
Katsu Ya (the Studio City location, not the SBE offshoots, awesome sushi and a legend)
Millese (A bit stuffy and over the top, but amazing food)
Soi 7 (Probably not the best Thai in LA, but I love the atmosphere and decor of the place, and the food's good)
8oz (Known for their burgers, I love the shortrib grilled cheese)
Bottega Louie (Food is really good if not particularly creative, pizzas are awesome, dining room is amazing)
Panini Cafe (5 star it's not, but great for a quick lunch in either BH or downtown)
Little Door (Great Med food, nice atmosphere, love the multiple dining rooms)
Drink:
Library Bar (Downtown, love the cucumber martini, really chill place)
La Descarga (Cuban rum bar in East Hollywood, awesome atmosphere)
Thompson Hotel in BH (Rooftop bar has nice atmosphere and view, drinks suck, come loaded)
7 Grand (If you love whiskey, you can't miss this one)
Roger Room (Speakeasy style bar, but I've had much better (and cheaper) prohibition-era cocktails in Chicago (where else?))
Coffee:
Spring for Coffee (downtown)
Luxxe Caffe (Santa Monica or Brentwood)
Espresso Profetta (Westwood)
El Carmen (This small Mexican dive on 3rd is not to be missed, great place to get in trouble)