Does anyone know of a list of city roads with bad pavement ( NYC )
While New York City is at the moment quite bike-friendly, potholes, cracks, and patched roads are still problems. Unfortunately, there seems to be no single resource for finding smooth roads in the city. The best you can do may be to rely on information from several sources, and use your own experience to decide on how to use the information. 

Google Maps Traffic

Google Maps has a layer for traffic, and that shows ongoing road work. For example, this view of Manhattan has icons for road closures due to construction and other maintenance work to bridges and tunnels. 



While this won't tell you what areas simply have bad pavement, avoiding these areas will at the least help matters. 

NYC Bike Map

The impressive NYC Bike Map will help keep you to areas that are more suitable for cycling. However, from experience, I can tell you that not all of these have suitable pavement for skinny tires. (For example, the East Side Greenway is shown in green, and while it's quite rideable, the surface isn't the best and the path has many corners and even a staircase. At least, this was the case a year or two ago, the last time I rode it.)



The map also exists as a Google Maps/Google Earth layer, although whether it's current or not is another matter. 

Conclusion

In summary, riding the roads and learning them well is probably the best way to know where to ride. I suggest using these tools to get some information to guide where you ride until you learn the roads. You can also ask bike clubs and bike shops for further advice.