My spots are mostly just for the aesthetic and don't really showcase the park super well. If you didn't bring a buddy to take pictures for you, you can take self-timer photos in all of these spots.
The walls of Mel's Drive-In. Sunset, in particular, makes for really good lighting on any side of the building. You can either get just the teal color if you're doing it purple wall-style by using one of the columns as a stand, or if you do it next to the platform (stage?), you can get the window/some interior lights/some of the neon signs in the background.
Horror Make-Up Show. If you prop your phone/camera on the other side of the Mel's platform thing, you can get some interesting angles with Hollywood in the background. Again, sunset makes this area light up dramatically and causes cool, strong shadows.
The waterside area just below the smoking area near Central Park. Not only is this walkway dead because the guests are perusing the park and the smokers are under the shelter, but this spot with the benches can give you some of the cityscape of San Francisco in a way that makes it feel less like a park and more like a real environment. You also get some of the lagoon itself, which is cool.
Sting Alley, ESPECIALLY during HHN. The area in general can is a good backdrop, but the fog machine added next to the van makes it extra dramatic.
Shortcut walkaway near Animal Actors. This is HHN-specific. There are some really cool red and blue lights that make for a fun use of color. It's only at night, of course, and I don't know if the lights are like that all year or not.
Examples: