How to serve static files from a different directory than the static path?

You need to wrap favicon.ico with parenthesis and escape the period in the regular expression. Your code will become

favicon_path = '/path/to/favicon.ico' # Actually the directory containing the favicon.ico file

settings = {
    'debug': True, 
    'static_path': os.path.join(PATH, 'static')}

handlers = [
    (r'/', WebHandler),
    (r'/(favicon\.ico)', tornado.web.StaticFileHandler, {'path': favicon_path})]

application = tornado.web.Application(handlers, **settings)
application.listen(port)
tornado.ioloop.IOLoop.instance().start()

Delete static_path from the app settings.

Then set your handler like:

handlers = [
            (r'/(favicon\.ico)', tornado.web.StaticFileHandler, {'path': favicon_path_dir}),
            (r'/static/(.*)', tornado.web.StaticFileHandler, {'path': static_path_dir}),
            (r'/', WebHandler)
]