Bootstrap 3 Skeleton
HTML
<link rel="stylesheet" href="http://getbootstrap.com/dist/css/bootstrap.css">
<script src="http://getbootstrap.com/dist/js/bootstrap.js"></script>
<link rel="stylesheet" href="//maxcdn.bootstrapcdn.com/font-awesome/4.1.0/css/font-awesome.min.css">
<br /> <br />
<div class="container">
<div class="col-sm-8">
<div class="input-group">
<input type="TextBox" ID="datebox" Class="form-control"></input>
<div class="input-group-btn">
<button type="button" class="btn btn-primary dropdown-toggle" data-toggle="dropdown">
<span class="caret"></span>
</button>
<ul id="demolist" class="dropdown-menu">
<li><a href="#">A</a></li>
<li><a href="#">B</a></li>
<li><a href="#">C</a></li>
</ul>
</div>
</div>
</div>
</div>
CSS
@import url('http://getbootstrap.com/dist/css/bootstrap.css');
JavaScript
$('#demolist li').on('click', function(){
$('#datebox').val($(this).text());
});