Out of all the things to do in LA (there are tons!), one of my favorite is to dine. When it comes to lunch, Joan's on Third cannot be rivaled. Best Sandwiches ever (I go for the basil, mozzarella, tomato, on a baguette. It is perfectly peppered). Tons of people watching (and star sightings. Jeremy Piven was a lunch companion one day). The pastry case is among the best I have seen and the cupcakes are not to be missed. My personal favorite: Classic Vanilla.
It makes me think of Meryl Streep's restaurant/cafe in the movie It's Complicated (as pictured below).