I just noticed this while reading the forum to decide whether or not to switch to Dreamhost as my hosting provider, and I noticed your question.
I am a web designer and I use Joomla pretty extensively for many of my sites because my clients are decidedly not web-savvy and it helps them feel a little more in control of their content. So I felt the need to stop and answer your question since I know the answer.
The path to Joomla is only found in one file, configuration.php . Joomla.org's forums have more information on migrating from one directory or one host to another, but if you're doing it on the same server, same domain... you should have no trouble telling Joomla where its new home is.
Here's the code in Joomla's config file that tells it where its home is:
$mosConfig_absolute_path = '/home/bar/foo/public_html';
$mosConfig_live_site = 'http://www.foo.bar.org';
you would just change, I think, to:
$mosConfig_absolute_path = '/home/bar/joomla/public_html';
$mosConfig_live_site = 'http://www.joomla.bar.org';
I think that answers your question. I have only changed directories so far, not subdomains.
If you have trouble or you don't think you want to try, there is an extension at Joomla.org that has a commercial license that will allow you to copy an entire joomla site as a backup and then place it anywhere new that you want... even on a new host, etc. It's under $100, I think it's $35-50, not sure.