Just use $_GET when getting variables from the URL/query string.
This will work...
$uploaddir = '/home/httpd/vhosts/mysite/httpdocs/' . $_GET['category'] . '/images/';
You cannot put a variable inside '' and get the value of the variable, you have to put it in "" or end the '', then put the variable, then start '' again.
Like...
$var = 'foo';
echo 'This is ' . $var . 'bar';
# Results: This is foobar