I can't directly answer your question, but I was in a somewhat similar situation myself, so I'll share my experience.
For undergrad, I was choosing between UMass Amherst (which is ~25 minutes from my hometown) and the University of Michigan. My heart was deadset on Michigan throughout the admissions process, but unfortunately my acceptance came with no financial aid; going there would have put me in crippling debt (over $200,000!). Like you, my family told me that if I really wanted to go to Michigan, they could make it work. Ultimately, I didn't want to put them through that financial strain, so I decided to attend UMass. I was pretty disappointed at the time.
Fast forward 4 1/2 years, and I've graduated with a degree in Physics, over three years of research experience on multiple projects (including an REU), and I'm going to be attending Caltech in the Fall for theoretical physics.
From my experience, I would have to say that your undergraduate degree is what you make of it. The undergraduate curriculum at UMass is admittedly not the best in terms of rigor (and definitely biased towards experiment), but by studying hard, getting involved in research, taking honors courses, and taking some graduate courses, I feel plenty prepared for my graduate studies. In your case, U Washington is a very good school for physics (better than mine!); even if it is slanted towards engineering/mat sci, there are going to be plenty of resources for a fellow budding theorist to succeed and prepare. You just need to know where to look (and, perhaps more importantly, who to ask).
As for grad admissions - getting into a great program is going to require good-to-great grades, meaningful research experience, good-to-great GRE scores, and strong LORs, regardless of what undergrad school you come from. Attending UW will not hold you back, as long you're still doing these things. Great grades from UCSB may be looked on slightly more favorably by a committee, and you may be able to work with/get LORs from more famous people at UCSB, but that's about it (the latter of these two can potentially be a big advantage, but plenty of people get into elite schools every year without famous recommenders. You'd be surprised how well people in academia know each other.)
I guess the punchline for what I'm saying is that, from my experience, you can attend your "local" state school out of financial consideration and still set yourself up for a successful career in theory. I hope that helps you in your decision.