You can use ArcMap to help identify a coordinate system. Leave the CAD file with an unknown (undefined) coordinate system. Add it and some reference data (that does have a known coordinate system) to ArcMap.
You can now set the data frame's coordinate system to possible candidates. In the US, that would include various State Plane zones (in meters, US survey feet, or int'l feet), UTM zones, state-wide grid, etc. It's less likely that city data uses one of these because sometimes there's a city coordinate system that we (Esri) just hasn't heard about.
So as you set the data frame's coordinate system, the unknown data will continue to be displayed where it was. That is, the software can't do anything to it. The reference data will be projected to the new coordinate system. If you can get the reference data to line up with the CAD data, then you've discovered the coordinate system.
Another trick is to look at the coordinate values. If the X or Y values have at least 6 digits, then the data may well be using a 'known' coordinate system. Five or less usually means a local system.
Melita