Moving the site among directories/sub-directories
From Joomla! Documentation
Many times you install Joomla in a sub-directory and then want to move it to a higher level directory, here's a short tutorial on how to do it.
Say you have installed Joomla in the following folder: public_html/tryjoomla. Now that you are satisfied with the site, you'll want to move to public_html.
1. Move all the files from the sub-directory (i.e., public_html/tryjoomla) to the upper level directory (i.e., public_html). You can use your favourite FTP client or the control panel that your hosting service provides.
2. Download and open the configuration.php file in a text editor.
3. Look for the following variables
var $log_path
var $tmp_path
var $ftp_root
var $live_site
The first two will definitely have a long value; the other two might not. The first line will look similar to
var $log_path = '/home/username/public_html/tryjoomla/logs';
Change this to
var $log_path = '/home/username/public_html/logs';
We've simply removed the tryjoomla folder name from the path. Similarly change the tmp path
var $tmp_path = '/home/username/public_html/tmp';
If you have the $live_site and $ftp_root variables with some values, they too need to give up the tryjoomla folder, so they can look something like
var $live_site = 'http://www.yoursite.com/tryjoomla';
becomes
var $live_site = 'http://www.yoursite.com';
AND
var $ftp_root = 'public_html/tryjoomla';
becomes
var $ftp_root = 'public_html';
If you have cache enabled, login to the administrator backend (which will now be at http://www.yoursite.com/administrator and not http://www.yoursite.com/tryjoomla/administrator). Go to Tools -> Clean Cache and delete all cache files.