this page http://maps.huge.info/trace.htm would give you all the coordinates, but it would involve clicking alot to draw a city map, and then the data would have to be modified to put into an xml (or other file format) to include names for the specific line, and change colors, and so on. and keeping track of which line was which street would be difficult.
Illustrator is probably the better route.
I am really curious now, as your fictional city has a real world location, were you intending to display it in google maps, or just looking to see if it could be leveraged to draw it.

As far as saving a nickel, Qgis is free, and with plugins will allow digitizing shape/vector files. And you could load your area of New Jersey from a WMS server to trace over,,,,I am sure someone has mapped New Jersey by now

But that would be back to drawing.