Maybe something like this ?
<?php
$query = "SELECT DISTINCT event_date FROM events WHERE event_date='$todaysdate'";
$result = mysql_query($query);
while($row = mysql_fetch_assoc($result))
{
echo "<b>". $row['event_date'] . "</b><br />";
$query2 = "SELECT event_name FROM events WHERE event_date='$todaysdate'";
$result2 = mysql_query($query2);
while($row2 = mysql_fetch_assoc($result2))
{
echo $row2['event_name'] . "<br />";
}
echo "<br />";
}
?>