Moving a Drupal installation to a subdirectory
You can use the module Pathologic that acts as a filter on your text formats (Full HTML, Filtered HTML) and basically rewrites URL's which are parts of fields depending the site configuration and Pathologic settings.

You can for example set Processed URL format to Path relative to server root (/foo/bar) and for the All base paths for this site, you fill in the different website URL's.