Google was just a proxy for software engineering employers who pay well. Microsoft, Facebook, Amazon all pay similarly. So do a number of other companies. The finance corps in NYC probably do too, but I wouldn't really want to work there either from what I've heard.
Regardless, I certainly would not encourage you or anyone else to leave a job they love if it pays them an amount they are happy with. Going to Google or anyone else for a 20% pay bump is a bad deal if you end up less happy overall.
It's good to keep in mind that "software engineering employers who pay well" don't necessarily pay everyone that well, or even most of their employees. My guess is that very few Googlers get that mystical $200K (although no doubt someone will reply here with an example to "prove" me wrong). Always comparing your salary (or as a business owner, what you offer your employees) to what Google pays the top 0.1% of their talent is bound to leave you disappointed.
The $200K level is really, really not mythical in NY. Many software jobs at all kinds of companies, ranging from start-ups to pure tech firms to food service organizations to finance companies to advertising firms will pay a software developer around $200K/yr in base pay, and usually there is some opportunity for bonus and equity as well. You probably also only need 3-4 years of experience to get your name in the hat for these positions too; I'm not talking about only developers with like 10 years of experience.
To put it in perspective, I earned a base salary in the very high $100K's when working for a large education company in Boston, having only 3.5 years of experience at the time.
The cost of living in New York is something like 30% higher than Boston, so before I would even consider any job in New York at all, even just to keep my wage at the same level relative to cost of living, you're talking about a salary certainly above $200k. Sure, places are free to dupe youngsters who just think it's cool to live in NY and are happy to take a discounted salary in order to get that personally-valued benefit. But a lot of thoughtful people who would make great employees for you won't do that -- won't even consider your job at all or do any of the hiring process unless they know it at minimum offers them a pay level that keeps their quality of life consistent. Otherwise they'll just stay where they are, or they'll work in some different geographic area where the pay isn't so distorted from the true cost of living as in New York.
I do love all the work that Stack Exchange does to keep using fully private offices though. Despite disagreeing with the salary levels, I would still say Stack Exchange is one of the best organizations around purely because it's like the last bastion of hope that we might move away from the demonstrably unhealthy dystopia of open-plan office madness, and further because they're in Manhattan, they help eliminate the demonstrably incorrect claim that a lot of places make, which is the excuse that they need open-plan offices because of real estate costs.
Interns at Facebook make about $100k, and they get free luxury housing. I know people at Google at Facebook. New grads make about 170k per year (total compensation), next level is about 220k, and the next (which is Senior) about 300k. One level above that (ie Staff Engineer) gets into the 400-500k range. $200k is definitely about average pay for Google engineers (maybe $150k is more accurate for offices outside MTV/NY/SEA).
No doubt. I'm would not expect that most devs at Google are getting paid $200k. I would expect that the top-of-the-top (i.e. the '5s' here) are getting paid $200k and more, though. Basically, I feel like the entry-level pay here looks reasonably competitive, but the senior pay looks low relative to my experience and what I know of others' salaries and salary ranges. This is of course largely anecdotal, so maybe I'm wrong, but I don't think so.
Regardless, I certainly would not encourage you or anyone else to leave a job they love if it pays them an amount they are happy with. Going to Google or anyone else for a 20% pay bump is a bad deal if you end up less happy overall.