How do I hide an element on a click event anywhere outside of the element?

If I understand, you want to hide a div when you click anywhere but the div, and if you do click while over the div, then it should NOT close. You can do that with this code:

$(document).click(function() {
    alert("me");
});
$(".myDiv").click(function(e) {
    e.stopPropagation(); // This is the preferred method.
    return false;        // This should not be used unless you do not want
                         // any click events registering inside the div
});

This binds the click to the entire page, but if you click on the div in question, it will cancel the click event.

Try this

 $('.myDiv').click(function(e) { //button click class name is myDiv
  e.stopPropagation();
 })

 $(function(){
  $(document).click(function(){  
  $('.myDiv').hide(); //hide the button

  });
});

I use class name instead of ID, because in asp.net you have to worry about the extra stuff .net attaches to the id

EDIT- Since you added a another piece, it would work like this:

 $('.myDiv').click(function() { //button click class name is myDiv
  e.stopPropagation();
 })

 $(function(){
  $('.openDiv').click(function() {
  $('.myDiv').show(); 

  });
  $(document).click(function(){  
  $('.myDiv').hide(); //hide the button

  });
});