I have a perhaps very simple ArcGIS question: How can I make the road line segments start or stop at the edge of the city's Census Block Groups?
You can you the Clip (Analysis) tool, use this tool to cut out a piece of one feature class using one or more of the features in another feature class as a cookie cutter. You can read up more here as provided by ESRI. Also, keep in mind, the attribute values from the input feature classes will be copied to the output feature class. Here are a few examples ESRO provides as visual representation of the Clip tool.
A polygon shapefile clipped by another polygon shapefile
A polyline shapefile clipped by a polygon shapefile
A point shapefile clipped by a polygon shapefile