Snippet for http://stackoverflow.com/questions/28926980/polymer-accessing-dom-input-element-inside-a-custom-element

proto-element.html

<link rel="import" href="../bower_components/polymer/polymer.html">
<script src="../js/snap.svg-min.js"></script>
<script src="../js/jquery-1.11.2.min.js"></script>
<polymer-element name="proto-element">
<template>
	<div class="div2">
		Source:<input type="text" id="textsrc" value="SOURCE"><br>
		Destination: <input type="text" id="textdest"><br> Flight:<input
			type="text" id="textplane"><br>
	</div>
</template>
<script>
        Polymer('proto-element',{ 
          ready: function() {
                var s = Snap(900,700);
                var rec1 = s.rect(50,200,150,80);
                var rec2 = s.rect(350,200,150,80);
                    rec1.attr({
                      fill: 'lightblue',
                      stroke: 'lightblue',
                      strokeOpacity: .3,
                      strokeWidth: 10,
                      id : 'id111' 
                    });


                    rec2.attr({
                      fill: 'lightblue',
                      stroke: 'lightblue',
                      strokeOpacity: .3,
                      strokeWidth: 10,
                      id : 'id112' 
                    });

                var hackthis = this;
		    	document.querySelector('#id111').addEventListener('click', function(e) {
		    		var txtboxval = hackthis.$.textsrc;
		    		alert(txtboxval.value);
		      	});
          }
    });
</script>
</polymer-element>