The designers over at Pop Chart Lab have put together a sharp-looking, albeit somewhat arbitrary map of over 200 "distinguished" New York bars, broken down by category (click here for a larger version). If you have a lot of money and plan on living in the city for a couple years, you should check them all out.
The map takes a pretty narrow view of "New York," omitting most of Brooklyn and Queens, Manhattan north of 103rd street, and two boroughs entirely—and even some of the more gentrified parts of Brooklyn are notably bare. Nevertheless, I have been to some of these bars, and can attest to the fact that they are great, and not necessarily super expensive, by NYC standards.
Mad that your favorite bar isn't on there? Don't be! You don't want people finding out about your favorite bar.