anche se ho seri dubbi su come intendi usare questa pagina,
eccoti il codice. vedi se cosi va.

codice:
<?
$connessione = mysql_connect("localhost", "root", "password")
or die("Connessione non riuscita");
mysql_select_db("design");
?>
<script type="text/javascript">
function inviaCambiamenti(){
document.form.action = "<? echo $PHP_SELF; ?>";
document.submit();
}
</script>
<h1>Store locator</h1>

<form name="search" method="post" action="ricerca_store_ris.php">


<h2>Select a store :</h2></p>



Continent:</p>
<select name="sel_continent" style="width:432" onchange="inviaCambiamenti()" >
<option value="none" >select Continent</option>
<?
$query_continent="SELECT DISTINCT continent FROM store";
$ris_continent = mysql_query($query_continent) or die("Query fallita");

while($row_continent=mysql_fetch_array($ris_continent)){
if($row_continent['continent']!="null"){
$continent = $row_continent['continent']; /*variabile in cui voglio mettere il continente selezionato per fare la prossima query*/?>

<option value='<?=row_continent['continent']?>'> <?=row_continent['continent']?>

</option>
<? } }?>
</select>



Nation:</p>
<select name="sel_nation" style="width:432" onchange="inviaCambiamenti()">
<option value="none" >select Nation</option><?
if(@$_POST['sel_continent']!='none';){
$continent=$_POST['sel_continent'];
}
$query_nation="SELECT DISTINCT nation FROM store where continent = '$continent'";
$ris_nation = mysql_query($query_nation) or die("Query fallita");

while($row_nation=mysql_fetch_array($ris)){
if($row_nation['nation']!="null"){
$nation = $row_nation['nation'];/*variabile in cui voglio mettere la nazione selezionata per fare la prossima query*/?>

<option value='<?=$row_nation['nation'?>'> <?=$row_nation['nation']?>

</option>
<? } }?>
</select>



Country:</p>
<select name="sel_country" style="width:432" >
<option value="none" >select Country</option><?

if(@$_POST['sel_nation']!='none';){
$nation=$_POST['sel_nation'];
}
$query_country="SELECT country FROM store where nation = '$nation'";
$ris_country = mysql_query($query_country) or die("Query fallita");

while($row_country=mysql_fetch_array($ris_country)){
if($row_country['country']!="null"){ ?>

<option value='<?=$row_country['country']?>'> <?=$row_country['country']?>

</option>
<? } }?>
</select>

<input type="reset" name="reset" value="reset">
<input type="submit" name="lanciaform" value="start">

</form>
cmq cosi dovrebbe fare quello che chiedi (penso)