If I'm interpreting your question correctly, maybe this is what you're after:
Put your event handling code inside the click event for the menu item, and call preventDefault() at the end of that click event. You won't need both the click handler and the select: handler.
$mymenu.find("a").click(function(event){
// event handling code - alert($(event.target).text());
event.preventDefault();
});
Anything you want to run on the click will still run, but the link will not be followed.