You can use the ZipCodeAPI for Zip Code Radius to find all zip codes within a given radius of a zip code.
Try out the ZipCodeAPI entering a zip code and radius: 
We always love to hear how people are using ZipCodeAPI. One customer is a large online car resale website. It let’s the buyer look within a radius of their zip code for available cars.
Share how you are using the Zip Code API, even if it is for free. Hopefully it will give others some good ideas!