Make a select where the options are the different multisites

This method will give you a select menu of active blogs.

function list_all_blogs() {
    global $wpdb;
    $query = "SELECT blog_id FROM " . $wpdb->base_prefix . "blogs WHERE spam != '1' AND archived != '1' AND deleted != '1' AND public="1" AND blog_id != '1' ORDER BY path";
    $blogs = $wpdb->get_results($query);
    echo '<select id="blog-select">';
    foreach($blogs as $blog) {
        $blog_details = get_blog_details($blog->blog_id);
        echo '<option value="'. $blog_details->siteurl .'">' . $blog_details->blogname .'</option>';
    }
    echo '</select>';
}
//call the method
list_all_blogs();

You’ll need to create a script to navigate to the page on menu select. Something like this:

<script>
$(document).ready(function($){
    $('#blog-select').change(function(){
        window.location.replace( $(this).val() );
    });
});
</script>

There are definitely other ways to accomplish this and perhaps more effecient approaches but I hope this helps.