I don't really care if working for Google increases my market value, since I'm not sure I would want to leave Google once there. So it makes sense to me to get salary sorted out now, and then move to Google. If I passed the interview once I can probably do it again.
The reality is, if I didn't have to move, I would have accepted Google's offer instantly. But New York is expensive, and moving is a huge pain, and so the value isn't there to make me think, "yes, I must do this". I don't want to coordinate movers and look for apartments; I want to ride my bike and write software.
(Something that was strange about the Google negotiation process was that they only tried to match Amazon's Seattle offer; they never asked me what I wanted in order to move to New York. Take it or leave it, not negotiable. So if I can get what Google offered me from my current employer, it works out better for me in the short term.)
Edit: as it turns out, my current employer "can't" match my offer at Google. So, I'm moving to New York :)
2) I'd hate New York also, but you're not moving there for the rest of your life. I know people who've moved from Mountain View or San Francisco offices to Seattle offices, and vice-versa while staying at Google. The Cambridge Office is quite nice as well.
I personally don't like Bay Area at all (San Francisco is disgusting, rest of Bay Area feels like you're stuck in a bad 70s movie), but there are only a few metropolitan area where software engineers are appreciated.
3) Just do it: I saw your comments on this site, I saw your Github repositories. You'll find actual culture fit at Google, something you won't be able to appreciate until you actually have it (or, on the flip side, as I found out myself -- until you've lost it and found it again).
Just don't use working at Google as an excuse to stop working on personal projects.