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.