I live in Seattle and went to school in Boston, and really wish I had considered looking at UW. It's a great school, the city is awesome, the campus is cool (urban and happening, but still lots of green space) and the engineering programs are really good. Seattle is one of the best ski cities in the country as long as you are down to wear gore tex and wanna ski rowdy fuckin terrain. def give UW strong consideration, and also consider studying computer science, its more engaging than mech E (IMO) and pays like twice as much.
The great myth of the world is that mechanical engineers make cool stuff, when really the vast majority of them design like a small piece of a pump or something (aerospace excluded, but those jobs are few and far between, in great demand, and also dont pay nearly as well as software). Sorry for going off topic...consider UW