How can I edit the html of the title of my node page
Depending on your current theme, the title may be found in the node.tpl.php, the page.tpl.php (usually this one) or html.tpl.php. Enable theme debugging to toggle theme debug comments. That way, you see which templates control which portions of the page.

Add the following to settings.php and refresh a couple of times (clear cache if it becomes stubborn). Then inspect the page.

$conf['theme_debug'] = true;


With theme debugging on, you'll also see the progression of template name suggestions in the comments, with the top most/most specific/longest name being selected first. 

You can also add to this list by altering the theme_hook_suggestions property in the variables argument of the appropriate hook_preprocess_ hook. If I remember correctly, there's no suggestion content type suggestion for templates. If so, you'll have to add one.