Go to the school that you like the most. Princeton is easily the best school of that bunch, and will give you the best chance at the best education. The people you'll meet, the profs you'll have, the opportunities that will be available to you out of Princeton over the next four years (and, heck, to a lesser extent, for life) -- that's all priceless. So, assuming you like every school equally, Princeton is the correct call. Chances are you won't end up at law school from any of them--some incredibly high percentage (95%?) of incoming college students end up pursuing a different career than what they say they're interested in as a pre-frosh--but the undergrad degree and, more importantly, the education you'll get at Princeton is something that you do know about at this point. That doesn't mean that you can't get a good education at USC (or any of the other places you listed) -- you almost certainly will -- but the education you'll get at Princeton will most likely be better. That said, my original advice stands: if you like USC or Wash U more, go there -- these are all three good enough schools that you'll be better off happy at a place that fits you right than at the "best" school (that fits you poorly). Put another way, you'll do better happy at Wash U then you will sad at Princeton.
Incidentally, there were a ton of Princeton kids at my law school. I can only think of one USC grad, and I'm not sure if there were any Wash U grads. The whole "go to an undergrad where you can get straight As and then go to HYS" thing only works if you (1) get straight As and (2) still do really well on the LSAT, which are both big ifs (and (2) is likely causally related to the quality of your undergrad). It also misses the point of undergrad, which should be some of the most educationally and personally formative years of your life (rather than merely a stepping stone to a career). There are a ton of 3.8+ GPA law school applicants from lower tier schools each year, and yet HYS are largely filled with people from schools like Princeton. There's a reason for that. Now, Wash U and USC are far from lower tier, but the point I'm exaggerating to make obvious nevertheless applies in this circumstance, albeit to a lesser extent.
**I'm a HYS law grad and I did not go to Princeton or any Ivy for undergrad, so take my comments with whatever grain of salt you think is necessary.**