I'm amazed poster spent so long discussing Peets when there are tons of fabulous LA coffee joints. These may be a little too "upscale" but LAmill and Intelligentisa in Silverlake are both delicious. They make strong, flavorful coffee without any bitterness.
Lamill also has amazing desserts....and the mythical syhpon method. They are both more expensive than your average cup, but not outlandish. Highly recommend them both if you love coffee like some love wine.