LA, or SoCal in general is known more for good restaurant options, nice weather all year round, upscale parties, 24/7 traffic, but unfortunately, the place doesn't have much to offer when it comes to tourist attractions.
I'd recommend flying to SF instead, spend a day or two exploring the
local attractions, then drive down to LA via the scenic route from
Highway 1 S to 101 S.
It's okay to spend a day or two in Vegas with your significant other, which is only a 3.5-4-hour drive with no traffic. Your SO doesn't have to be 21 to enjoy what the
town has to offer. As long as she doesn't look very young, and acts like she knows what she's doing, then she may even sit next to you while you play slots. I highly recommend going to at least one
Cirque Du Soleil show, like KA or Mystere; O is quite overrated IMHO.
Hope you have a safe and memorable trip!