Griffith park has always been one of my favorite places for photo shoots. One of the best things I love about this park is it's hugeness and variety. If you take time and start slowly exploring it you'll find so many scenes with different looks that you'll need at least one year to discover most of it. And the second best thing about it is that it has so many places that are covered with trees so that you can even shoot at noon (when the sun is at its highest position) and not get that harsh light effect with strong shadows and overexposed highlights. Another thing I like about it is that it's free, there is no submission fee or any other surprise charges. It's a huge park and even if you're not planning to do photoshoots there you should definitely check it out.
If you know and other beautiful places to shoot in LA please share the info in the comments :)