How do you change the Document Root from http://myIP/MySite to http://myIP

I don’t know about nginx but for Apache it is very simple if you really just want to redirect from http://your.server/ to http://your.server/your_site and you only have that single site.

Just add

RedirectMatch ^/$ /your_site/

to your

<VirtualHost *:80>
    …
</VirtualHost>

definition below /etc/apache2/sites-enabled and restart Apache. But of course @Anders suggestion is much more sophisticated.