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You will need longitude / latitude co-ordinates for each postcode. Then you can use the haversine formula to find things within a given distance of an originating point. Websites like Google Maps use this for instance when you need the distance between point A and point B.

 

Resources

http://en.wikipedia.org/wiki/Haversine_formula

http://www.pjenkins.co.uk/blog/index.php/2007/04/04/uk_post_code_distance_calculation/

(doesn't matter that it is UK, same formula)

 

Also take a look at:

http://www.booking.com/city/gb/london.html

You can see the formula in action. The blue module on the left shows places and landmarks that are near the current location (I think it is a 12km radius).

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