Given a database that contains three fields:
Latitude Longitude Proximity
Where Lat and Long are GPS coordinates, and Proximity is (some unit - feet? Seconds? Mi
The Haversine formula is what you want. Using simple Euclidian distance formula isn't sufficient, because the curvature of the earth affects the distance between two points.
Creating a Store Locator with PHP, MySQL & Google Maps is an article about implementing this solution with MySQL, but SQLite doesn't support trig functions.
Check out the answers in Calculating Great-Circle Distance with SQLite here on Stack Overflow for further tips on extending SQLite functions so you can solve this.