ArcMap... assumed (similar for Pro)
You have the point as a layer or a selection in a layer of intersections... assumed
You have the census data at the required level of detail you need in polygon form... assumed
You have many options: start with Select Layer By Location—Help | ArcGIS for Desktop
whereby you can select the census data within a distance of the intersection using all the polygons that intersect/are completely within/whatever choice you want.
Once you have the selection you can save it as a new layer, summarize the statistics within the table Summarizing data in a table—Help | ArcGIS for Desktop and a variety of other things.
More details if this doesn't suffice as a start
