I used to work at a print company. One of the documents we produced was a healthcare packet. Inside it had a listing of the 12 closest pharmacies from your location. We sent the zip codes to an outside company and they returned the 12 pharmacies. They used a zip to zip distance calculation.
If you want to do something like this on your own I know the census bureau or the post office has a database of zip codes and distances (or values you can use to determine distance.). I would start there.