Walking north up to La Cienega and Melrose (~10 minutes), I'm a big fan of Taste on Melrose, east of La Cienega.
West from La Cienega, you've got Urth Caffe-- sandwiches, salads, great coffee and pastries, and a scene-- and Le Pain Quotidien (of which I am NOT a fan but many others are).
Breadbar, Joan's on Third, Lemonade [9001 Beverly @ Almont] and Little Next Door are all relatively close, though, of the four, only Breadbar and Joan's would probably be considered walkable by most.
8164 West 3rd Street, Los Angeles, CA 90048
Joan's On Third
8436 W 3rd St, Los Angeles, CA 90048
8718 W 3rd Street, Los Angeles, CA 90048