Is there any way to get the admin path for a given installation? Most of the time is /admin, but I want to know if there is a certain way to get the path of the admin programmatically.
You should use,
To get the Adminhtml Frontname in Magento local.xml try
<admin> <routers> <adminhtml> <args> <frontName><![CDATA[admin]]></frontName> </args>