How to search nearby places stored in my database?

You can use what is called the Haversine formula.

$sql = "SELECT *, ( 3959 * acos( cos( radians(" . $lat . ") ) * cos( radians( lat ) ) * cos( radians( lng ) - radians(" . $lng . ") ) + sin( radians(" . $lat . ") ) * sin( radians( lat ) ) ) ) AS distance FROM your_table HAVING distance < 5";

Where $lat and $lng are the coordinates of your point, and lat / lng are your table columns. The above will list the locations within a 5 nm range. Replace 3959 by 6371 to change to kilometers.