Here is a rough map of typical departure (and arrival) procedures in the San Francisco Bay Area:



Typically departures to LAX are assigned the PORTE3 departure, which involves an immediate left turn on departure. In my experience, this typically happens south of the city, which leaves no seat with a good view of the city (left side will see it for a few seconds after takeoff, but really far away, and the right side will see blue sky).

As others have mentioned, runway choice will depend largely on the type of aircraft, but a lightly loaded 777 (such as one only going to LAX) might use 1L/R rather than the typical 28R too, so it's not all dependent on aircraft type. Weather will also play a significant factor. In mid-afternoon (2-5pm ish), winds often pick up, and 28L/R will be the only runways in use.

I'd probably agree with the left side recommendation, but I wouldn't get your hopes up too much either way. Good luck!