I did this exact thing in 1st year geography. Gotta use the network analysis tool, not spatial analysis. Distance along road segments, not the Euclidean distance tool.
You can take a shortcut, because NYC is several large grids stitched together. If your isochron line doesn't cross a border between two grids its just a diamond instead of a circle. If it does cross the border between two grids, then you just have to figure out where along the border the "diamond" of one grid system meets the tilted diamond of the other. But you don't need a general purpose road network analysis tool to do it. It may even be tractable analytically.
