The issue is likely due to the calculation of $(this).offset() is based on the position of the "option" element and not the parent "select" that I'm guessing you're wanting to target.
Consider this approach:
var parentOffset;
if($(this).is('option'))
parentOffset = $(this).parent().offset();
else
parentOffset = $(this).offset();
UPDATE:
$(".topLeftNavBarInner").click(function(e){
var parentOffset = $(this).offset();
var relX = parentOffset.left-140;
var relY;
if(e.target.nodeName=='OPTION') {
var selectOffset = $(e.target).parent().offset();
relY = selectOffset.top;
}
else
relY = e.pageY-15;
$(".FloatingUpdateSearchResultsDiv").show();
$(".FloatingUpdateSearchResultsDiv").css({position:"absolute",left:relX,top:relY});
});
You may still choose to manipulate the "relY" value in the case of an OPTION being the source of the click but this should keep the floating DIV in the area you want.