I think its somewhat of a risky move to use the "family is tying me down" part. It would be okay if you phrased it as a bonus, for example "I am a very family-oriented person and since most of my family is here in Washington, it will be icing on the cake to be able to pursue my dream and still be near family." Or something like that.
The question is more aptly phrased "Out of the 120+ medical schools in the US, you chose to apply to our school. What was it about
us that led you to that decision? Have you done your research? Do you know what our school is about? Have you thought about who you want to be as a doctor? Do the two go well together? How so?" At least that's how I took it. They realize that practically, of course its easiest for Washington residents to come to their school, its closer to home and family, its in at least somewhat familiar territory, the tuition is vastly less expensive...They know all this. What they want to know is that sure, you'd move to a tiny town in the middle of nowhere on the east coast if that's what it would take for you to be a doctor, but that you want to come to their school because of THEM not just whats going on in your life (even if that is your main reason). Basically, they want you to say, if all medical schools were PRACTICALLY (tuition cost, location, etc.) equal, what is it about us that made you apply?
Also, you're not that late, believe it or not! When I applied last year I wasn't complete until the end of September, got an interview invite 2 weeks later and went to the interview 2 weeks after that (another 2 weeks and I was on hold, all the way until the very last minute when I finally got the axe, but that was my own fault).
Anyway, I hope this helps! Good luck!