<?php
    if ( in_category( 'new-events' ) && in_category( 'old-events' ) ) {?>

//styling for this category
  <style type="text/css">
	#eventLocation {
	    background:url(/wp-content/themes/mytheme/images/myimage2.png) no-repeat left 2px;
		}
  </style>

<?php } elseif ( in_category( 'new-events' )) {?>
//styling for this category
  <style type="text/css">
	#eventLocation {
	    background:url(/wp-content/themes/mytheme/images/myimage1.png) no-repeat left 2px;
		}
  </style>

<?php } else { ?>
<?php } ?>