Installing WordPress in a Sub-Folder (not in root) on Localhost

Why don’t you use WordPress core settings for doing this?
This is the recommended way and doesn’t need editing .htaccess or Apache config directly. You can find the details here in WP docs. I’m posting the steps here:

• After installing WP in the root dir, Go to the Settings->General and change these values:
• WordPress Address (URL): http://localhost/wordpress
• Site Address (URL): http://localhost
• Save the settings and don’t worry about the errors
• Move all WP files to the wordpress sub-directory.
• Copy (NOT MOVE!) the index.php and .htaccess files from the wordpress sub-directory into the root directory of your site
• Edit the index.php placed in the root and change the line that says:
  require( dirname( __FILE__ ) . '/wp-blog-header.php' );
  to the following:
  require( dirname( __FILE__ ) . '/wordpress/wp-blog-header.php' );
• Login to WP using http://localhost/wordpress/wp-admin/
• Go to the Settings->Permalinks and save the settings (with no edit). This will regenerate .htaccess file in the sub-directory to include /wordpress path in it)

Now everything should work fine.

UPDATE: When you save the Permalinks, .htaccess file in the sub-directory would be something like this:

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /wordpress/
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /wordpress/index.php [L]
</IfModule>

# END WordPress

And .htaccess in the root directory:

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

# END WordPress

Note the differences in RewriteBase rule and the last RewriteRule rule. By adding these lines, WP would tell Apache, how to load the website by accessing the root directory of localhost (in addition to the edit in the root index.php). These .htaccess files are the reason that there’s is no need to re-configure Apache.

UPDATE2: I usually use XAMPP on Windows, and Apache rewrite_module is activated bu default on it. Digging around WAMP, I found that this module isn’t activated by default on WAMP. This may be the reason .htaccess files are not working on your setup. See these links to activate this module. [1] , [2]

I hope this would help you.