Firstly, get the value of the city. The value of the option should be the city ID. Then query the data base for the city_id in the hotel table, then return the results. E.g.
$cityId = $_POST['city'];
$result = mysql_query("SELECT * FROM `hotel` WHERE `city_id` = '".$cityId."'");
if($result)
{
if(mysql_num_rows($result) == 0)
echo "<option>There are no hotels!</option>";
else
{
while($hotel = mysql_fetch_array($result)
{
echo "<option value="".$hotel["hotel_id"]."">".$hotel["hotel_name"]."</option>";
}
}
}