Right, I've had a look around and I can't actually find a decent solution that simply provides you with the name of the group that the user belongs to. Everything else gives you an array or the ID, so I have written a simple function that will get you exactly what you want:
function getUserGroup($userId){
$db = JFactory::getDbo();
$query = $db->getQuery(true);
$query->select('title')
->from('#__user_usergroup_map AS map')
->where('map.user_id = '.(int) $userId)
->leftJoin('#__usergroups AS a ON a.id = map.group_id');
$db->setQuery($query);
$result = $db->loadResult();
return $result;
}
echo getUserGroup($user->id);
Hope this helps