You can add 'Content Editor' web part to your page, and in page edit view, select that web part and click 'edit HTML' in the ribbon. Then you just simly write html with javascript and css in that webpart :) so you can put <select>
tag with <option>
inside of it to create a dropdown, and then write javascript or jQuery, to navigate when that dropdown's value changes :) Here's the examples of dropdown in HTML: select example, and here's the example on how to use jQuerys's method .change()
on that dropdown: jQuery .change(). Good luck :)
EDIT:
For example add this to content editor webpart's html and see how it works:
<select id="mySelect">
<option value="-">-</option>
<option value="http://www.google.com">Google</option>
<option value="http://www.facebook.com">Facebook</option>
</select>
<script src="//code.jquery.com/jquery-1.10.2.min.js"></script>
<script type="text/javascript">
$(document).ready(function() {
$("#mySelect").change(function(){
if ($(this).val()!='') {
window.location.href=$(this).val();
}
});
});
</script>