I live in the NW, but our son lives in downtown LA right across the Staples Center. You can start with Googling the Disney Music Center. This is probably the most photographed building in LA since its opening in 2003. As our son has said, ever time he drives pass the building, there is someone taking pictures (day or night!). Near this building (which is on a "hill") are many other photo-worthy buildings (Dorothy Chandler Center, the Library, etc.).
The area around the Staples Center is also nice. The LA Live complex (across the street from the Staples Center) is almost complete with the Nokia Center, ESPN's western studios and the uber expensive Ritz-Carlton Residence condos. To the north of LA Live are 3 building walls that are used as large billboards (about 10 stories high??). When we were there in May, the billboards had characters in a video game. Our son said that these were changed for Michael Jackson's memorial service.
I don't know of any locations where you can shot the entire LA cityscape since I've seen it only from the freeways.
There must be POTNers in LA that know of such locations. Downtown LA is a much better shooting location than I expected.
Too much stuff, not enough shooting time.
Canon T4i (2 lenses), Fuji X100s, Olympus OM-D EM-1 (3 lenses)