One of my fav places in LA is The Grove. It's half modern shopping center, half a glimpse into LA's past. The newer part is filled with awesome shops and apartments (I would kill to live there!). It also has a two-story Barnes and Noble that I could spend hours wandering around in.
But my favorite part is the old farmer's market. It is filled with tons of fresh produce stands and has booths serving up any kind of food you can think of. It's a great place to people-watch (and stuff yourself silly with amazing food). I don't get to go there a lot because driving in LA scares the ever-living out of me, but everytime I do, I love it.