One of my favorite long runs in LA is from UCLA to the Venice Beach. I run through Westwood, then along Wilshire Blvd. under the 405 bridge. I then run along there until it becomes convient to turn right and onto San Vincente Blvd. Then, it is just a straight run until I reach Ocean Ave. which I run along until I can turn onto the beach at California Ave. I then run along the beach until I reach the Venice Beach Pier. The run is about 17km, so you would need to turn around and run backwards a bit to make it a half marathon.
My favorite medium length run is what I call the "Triangle Run". It starts near UCLA, and goes East along Wilshire Blvd. to Rodeo Drive. Then, you make a traingle, before running back. It is slighly hilly so it is good cardio training.