This is not hard once you have lat / long data, and if somebody gives you the great circle distance formula in mySQL format.
@maggie gave a good reference. How to efficiently find the closest locations nearby a given location
Indexing strategy: Keep in mind that one minute of latitude (1/60 degree) is one nautical mile, or 1.1515 statute miles (approximately) all over the world. So index your latitude column and do your search like this. (If you're in the part of the world that uses km, you can convert; sorry for the Old-British-Empire-Centric answer, but they did define the nautical mile.)
WHERE mylat BETWEEN column.lat-(myradius*1.1515) AND column.lat+(myradius*1.1515)
AND (the big distance formula) <= myradius
This will give you both decent data base indexing AND reasonably accurate distance circles.
One extra refinement: You can index longitude too. The trouble is that ground distance isn't directly related to longitude. At the equator it is one nautical mile per minute, but it gets smaller, and at the poles there are singularities. So, you can add another term to your WHERE. It gives correct results but isn't as selective as latitude indexing. But it still helps the indexing lookup, especially if you have lots of rows to sift through. So you get:
WHERE mylat BETWEEN column.lat-(myradius*1.1515) AND column.lat+(myradius*1.1515)
AND mylon BETWEEN column.lon-(myradius*1.1515) AND column.lon+(myradius*1.1515)
AND (the big distance formula) < myradius