function am2_cities_tax_create() {
    // this will add the custom meta field to the add new term page
    ?>
    <div class="form-field">
        <label for="term_meta[time_zone]">Time Zone</label>
        <input type="text" name="term_meta[time_zone]" id="term_meta[time_zone]" value="">
        <p class="description">If unusure, please check <a href="http://www.timeanddate.com/worldclock/">here.</a></p>
    </div>

<?php
}
add_action( 'cities_add_form_fields', 'am2_cities_tax_create', 10, 2 );


function am2_cities_tax_update($term) {
    // this will add the custom meta field to the update term page
    // put the term ID into a variable
    $t_id = $term->term_id;

    // retrieve the existing value(s) for this meta field. This returns an array
    $term_meta = get_option( "taxonomy_$t_id" );
    ?>
    <tr class="form-field">
        <th scope="row" valign="top"><label for="term_meta[time_zone]">Time Zone</label></th>
        <td>
            <input type="text" name="term_meta[time_zone]" id="term_meta[time_zone]" value="<?php echo esc_attr( $term_meta['time_zone'] ) ? esc_attr( $term_meta['time_zone'] ) : ''; ?>">
            <p class="description">If unusure, please check <a href="http://www.timeanddate.com/worldclock/">here.</a></p>
        </td>
    </tr>
<?php
}

add_action( 'cities_edit_form_fields', 'am2_cities_tax_update', 10, 2 );

function am2_cities_tax_custom_meta_save( $term_id ) {
    if ( isset( $_POST['term_meta'] ) ) {
        $t_id = $term_id;
        $term_meta = get_option( "taxonomy_$t_id" );
        $cat_keys = array_keys( $_POST['term_meta'] );
        foreach ( $cat_keys as $key ) {
            if ( isset ( $_POST['term_meta'][$key] ) ) {
                $term_meta[$key] = $_POST['term_meta'][$key];
            }
        }
        // Save the option array.
        update_option( "taxonomy_$t_id", $term_meta );
    }
}
add_action( 'edited_cities', 'am2_cities_tax_custom_meta_save', 10, 2 );
add_action( 'create_cities', 'am2_cities_tax_custom_meta_save', 10, 2 );