By default, boost stores its cache in the "cache" directory located at the root of the website.
A frequent request is to store the cache on a per-site directory under other files generated by the site, in sites/example.org/files/cache/, for example. However, this is likely to cause issues with how the Drupal htaccess rules for multi-site work.
Note that the default way boost stores the cache does support multi-sites. You should not need to change this setting unless you have specific requirements.
If you need to change the location of the cache:
- Go to admin/config/system/boost/filesystem,
- Change the "Root cache directory", for example, instead of "cache", you can use "sites/cache",
- Click on "Save configuration".
- Then go to admin/config/system/boost/htaccess/generator to get a new version of the htaccess rules to insert into your .htaccess.
If you want to store the cache outside your Drupal directory hierarchy, you will need to create a symlink to the real location or create an Apache alias.