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So, you need to do two things: convert zip codes into coordinates (called geotagging) and use these coordinates to find actual driving distances. Both of these will require some external services such as Geopy with the free Nominatim for geocoding and services such as the Mapbox Matrix API or Google Distance Matrix API for driving distances.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.