$wpdb doesn’t appear to work on page inside of a plugin

The $wpdb object is part of WordPress, so wouldn’t be loaded into a standalone PHP page as it is into a WordPress template.

You might want to look into creating your own page templates, then you could run your database query as part of that page template.

As a side note: You are currently trusting input from the user ($_REQUEST) which is a Bad Thing™, as it could make you vulnerable to SQL Injection attacks. The code example you give could be adapted as below to be less vulnerable:

global $wpdb;
$orderby = $_REQUEST['orderby'];
// Limit the values of orderby to ones we know to be safe
$acceptable_orderbys = array( 'name', 'age', 'height' );
if ( in_array( $orderby, $acceptable_orderbys ) )
    $clean_orderby = $orderby;
else
    $clean_orderby = 'name';
$sql = "SELECT * FROM wp_nc_location ORDER BY $clean_orderby";
$data = $wpdb->get_results($sql);

I’ve not tested the above code, but the key thing is to check the value of $orderby is known to be safe before you put it into the DB query.

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