Public Long-Term Parking Lot C is ideal for north runway as it is directly in the path of incoming airplanes for landing. The lot security is pretty relaxed about the enthusiasts photographing and although they come every 15 minutes protecting the lot, they just wave and let you be.
Radisson Hotel, I had a top floor southward view and it is a great view of the south side of the LAX and you can see the take off on that runway from start to finish. Only issue is there is a really baked purple colored film that's not optically nice, and although to spotting it's not a issue but it may be for any critical photography.
The In and Out is an exciting lot for getting close, but for photographers, it may be a bit TOO CLOSE as when they are near, they pretty much are too fast and too large, and you get a very good shot of every spec of dirt in the landing gear and tires. LOL!
Lookout point on the South end on Imperial Blvd is a cool place to get a big overview of the south complex. It's beautiful there at night too.
Embassy Suites South LAX used to be a nice hotel to shoot from 4th floor towards the south side of LAX, but tall trees cover most of the view now and its pretty much a luck of the draw to get a room that has a wide view into the airport. Also there is a nasty telephone/power cable in front that distracts photographer's frame as well.
The BEST point I know now is at this restaurant-weekend club called THE PROUD BIRD.
http://www.theproudbird.com/proudbird/
There are several WW2 warplanes parked there as a private collection, and the windows are crystal-clear for any photographer. The restaurant windows ALL look out toward the low sky of the VOR path of incoming south runway airplanes, and they fly directly in front of the window... Excellent vantage point and distance for photography. Also the fact that the window faces north, the sunlight is always perfect, hitting the planes just right no matter what time of day. about 4-6pm is when the sun is dramatic and the airplanes get lit well with nice dark red to purple sky.
If you go to the restaurant on slow days/hours, you can literally sit there for couple of hours with a nice meal. The meal can be pricey at night at about $50 a person, but the food is really on par with the price, and lunch is somewhat more reasonable. I love it there.
Do check with the restaurant though for weekends as they frequently get rented out to private parties for special occasions, and when that happens, its RSVP. Most of the weekdays are fine, and I recommend it to be the best place to see airplanes at LAX.