Top Tip
If you live in Colorado, rent a Post Office box in NYC so you can tell recruiters you're "in" NYC.
There's nothing to stop you from "moving" to Colorado later ;-)
Last time I was asked how much I was looking for, I gave them the figure for the average for the role in London, about 25% more than for the equivalent role in my area.
They agreed without question. In retrospect, as they also had equivalent roles in the US, I should have asked for the average for the role in the US as a starting point for negotiation!