I needed to move/restore my site to another server and subdirectory, and share my notes for the benefit of those with similar needs:
If you use search friendly URLs (e.g. Artio JoomSEF or OpenSEF (not on extensions.joomla.org but http://projects.j-prosolution.com/projects/os-projects/project-opensef.html), remember to modify the RewriteBase directive in .htaccess.
It's obvious that /configuration.php must be modified, but there are quite a few settings to remember. Off the top of my head: $mosConfig_absolute_path,
$mosConfig_cachepath, $mosConfig_db, $mosConfig_host,
$mosConfig_live_site, $mosConfig_user, $mosConfig_password...
A global search/replace for /oldsubdir to /newsubdir can be useful to alter any absolute URLs in .htaccess, templates or css, provided /oldsubdir is a reasonably uncommon string. I used the freeware editor PSPad for this: Search > Search/replace in files. (Hardcoded absolute URLs in content require similar modification, but I don't know any quick way to do this globally.)