Getting Harlan to take you on Mulholland Drive over to Lake Hollywood Park would provide a nice ride with some iconic views, but Harlen would be more knowledgeable about that specific area.
If you have the time, Mulholland Highway in the Santa Monica Mountains (just West of Los Angeles) and Angeles Crest Highway in the Angeles National Forrest (just North of Los Angeles) are a couple of signature rides for this area. The website
http://www.motorcycleroads.com/Routes/California_80.html has details and reviews on some area rides, but is by no means complete. Just about all of the canyons in the Santa Monica Mountains are fun in the day; not so much after dark. If you google the specific canyon road or search on YouTube, you can frequently find video's and reviews. I am not at all familiar with the area South of Los Angeles. I find it best to assume that any corner I cannot see around gets tighter, has rocks slide out onto the road with a bicyclist in the middle of the lane trying to get around the rocks and a car crossing over the double yellow in the other lane.
If you are not comfortable with heavy traffic, avoid the freeways as they can be quite unforgiving. The worst time is just off peak when the freeways are still full but moving at 70+. That 3 second gap you should maintain is just not going to happen.
Good luck and I hope you enjoy your trip.
Chocula