Moving the site among directories/sub-directories
From Joomla! Documentation
Many times you install Joomla in a subdirectory 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 public_html/tryjoomla folder. Now that you are satisfied with the site, you'll want to move to public_html.
1. Move all the files from the subdirectory (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 file manager that your hosting service provides.
2. Download and open the configuration.php file in a text editor.
3. Simply remove the tryjoomla folder name from the path. Look for these lines:
var $log_path = '/home/username/public_html/tryjoomla/administrator/logs';
var $tmp_path = '/home/username/public_html/tryjoomla/tmp';
Change to:
var $log_path = '/home/username/public_html/administrator/logs';
var $tmp_path = '/home/username/public_html/tmp';
N.B. The $live_site variable should not be given a value. If it was given a value during installation, edit that path as well, for example:
var $live_site = 'http://www.example.com';
Change to:
var $live_site = '';
4. Check your site's .htaccess file. The subfolder should be removed as well. The RewriteBase directive should be commented out. Check for a RewriteRule that contains the old subdirectory.
5. Verify that no redirect orders to the old subdirectory are in place in your hosting control panel.
If you have cache enabled, login to the Backend (which will now be at http://www.example.com/administrator and not http://www.example.com/tryjoomla/administrator). Go to Tools → Clean Cache and delete all cache files.