I've the next script:

$(document).ready(function() {
  $('#slideSelect').change(function(){
    $('#slideViewer img').attr('src', $(this).val() + '.png');
  });
});

Let me understand how the easiest method to give a Wordpress Template Tag would be to the #slideViewer img section.

Web site tag is:

<?php bloginfo('template_directory); ?>/builderimages/

Essentially I wish to finish with:

$('#slideViewer img').attr('src', TEMPLATE TAG HERE + $(this.val() + '.png');

You could attempt this:

var IMG_DIR = '<?php bloginfo('template_directory');?>/builderimages/';

// And then, later on...
$('#slideViewer img').attr('src', IMG_DIR + $(this).val() + '.png');

This will act as lengthy because the file using the var IMG_DIR part has been processed by PHP/WordPress. If required, you can put that inside a <script> inside your template's <head> section to ensure that it will likely be visible everywhere.

jQuery is client side while php code is server side. Which means you cannot directly interlink the 2. You will have to embed the data somewhere around the page to ensure that it may be retrieved by jquery. You can create any tag you would like after which retrieve something from it. This really is crude, but

//server side
<span id="templatesdir" style="display: none;"><?php echo bloginfo('template_directory'); ?></span>

//client side
var templates = $('#templatesdir').html();
$('#slideViewer img').attr('src', templates + $(this.val() + '.png');