Thanks so much for your thoughtful reply (and the illustrative metaphors)!
For points 1) and 3), I have always assumed that any geographical preferences would get tossed by the wayside in favor of my academic and professional ambitions. I don't really have strong personal feelings either way regarding east vs. west coast and Boston vs. Seattle. I think the one recurring location-related concern I have is that there's a much greater density of research institutions in the greater Boston area and in the east coast in general.
For point 2), again, I could go either way. I might want to do something related to statistical genetics, and my feeling is that Harvard has more high-profile people doing work in that area (and that UW's statistical genetics research tends to be more traditional, population-based stuff). On the other hand, I'm also interested in machine learning and optimization; UW would clearly provide more opportunities there.
I don't personally care too much about lay prestige, and the last thing I want to do is be the kind of person who decides stuff based solely on that. I don't intend to pursue a career outside of biostatistics/statistics, but God willing, I've got 40+ years of working ahead of me. That's a lot of time for me and the world to be certain about anything, but Harvard's name and reach are probably going to be evergreen. So the argument that people have made to me is that unless there is something specific that you really want to do that only UW offers, why would you turn down Harvard? And there's a certain logic there, because while it would be a mistake to choose a school based on lay prestige, it would also be a mistake to pretend that it doesn't exist.
As for theoretical rigor: I'm less concerned about surviving quals, so to speak, and more with whether or not having that kind of foundation serves people better in the long run. And I'm sure that it varies from person to person and is highly dependent on where on the theoretical-applied spectrum your interests fall. But unfortunately, I'm not quite ready to answer the question of how theoretical or applied I want to be.