How to go to tag archives using a form

To understand how to do it you first need to know how the url query works or more specifically what query vars you need, so:

• 'post_type' – to filter by post
  types.
• 'area' – to filter by area
  taxonomy.
• 'university' – to filter by
  university taxonomy.

so your url would look like:

//   http://www.domain.com/?post_type=properties&area=area_term&university=university_term

Now that we know we create the form with the needed fields:

function display_area_university_filter_form(){
?>
<form method="post" action="">
    <p><label for="area_t">Area: </label> <select name="area_t"><option value="">Select Area:</option>
    <?php 
        $area_terms =  get_categories('taxonomy=area'); 
        if (isset($_POST['area_t'])){
            foreach ($area_terms as $term) {
                $option = '<option value="'.$term->slug.'"';
                if ($_POST['area_t'] == $term->slug){
                    $option.= ' selected="selected"';
                }
                $option .= '>'.$term->name;
                $option .= '</option>';
                echo $option;
            }
        }else{
            foreach ($area_terms as $term) {
                $option = '<option value="'.$term->slug.'"';
                $option .= '>'.$term->name;
                $option .= '</option>';
                echo $option;
            }
        }
    ?>
    </select>
    </p>
    <p><label for="area_t">University: </label> <select name="area_t"><option value="">Select University:</option>
    <?php 
        $uni_terms =  get_categories('taxonomy=university'); 
        if (isset($_POST['univer'])){
            foreach ($uni_terms as $term) {
                $option = '<option value="'.$term->slug.'"';
                if ($_POST['univer'] == $term->slug){
                    $option.= ' selected="selected"';
                }
                $option .= '>'.$term->name;
                $option .= '</option>';
                echo $option;
            }
        }else{
            foreach ($uni_terms as $term) {
                $option = '<option value="'.$term->slug.'"';
                $option .= '>'.$term->name;
                $option .= '</option>';
                echo $option;
            }
        }
    ?>
    </select>
    </p>
    <input type="hidden" name="custom_filter" value="area_uni">
    <p><input type="submit" name="submit" value="submit"></p>
</form>
<?php }

then all that is left is just processing it:

if (isset($_POST['submit']) && isset($_POST['custom_filter']) && $_POST['custom_filter'] == "area_uni"){
    $url =  get_bloginfo('url');
    $area = $uni = '';
    if (isset($_POST['area_t'])){
        $area="&area=".$_POST['area_t'];
    }
    if (isset($_POST['univer'])){
        $uni = '&university='.$_POST['univer'];
    }

    $url .= '/?post_type=properties'.$area.$uni;

    wp_redirect( $url );
    exit();
}