How do I get the name and URL alias of a vocabulary using only  the vid? I need the URL alias of the vocabulary, not the term and not the machine name; I need the name that appears to the user.
You can use taxonomy_vocabulary_load() to obtain the machine name of a specific vid.

Example usage:

$vocabulary = taxonomy_vocabulary_load($vid);
$machine_name = $vocabulary-&gt;machine_name;
$name = $vocabulary-&gt;name;


Vocabularies aren't exposed to the user like terms are, so they don't really have an url-alias. The name which is presented in the vocabulary list is $name in the above code.