Adding pagination to sub-wp_query within a singular post page

You need to add a query var and rewrite rule to make that work.

First, add the query var to WordPress query vars array in your theme’s functions.php:

add_filter( 'query_vars', 'wpa58904_query_vars' );
function wpa58904_query_vars( $query_vars ){
    $query_vars[] = 'my_page';
    return $query_vars;
}

Then add a rewrite rule with your desired pattern that sets your custom page query var:

add_action( 'init', 'wpa58904_rewrites' );
function wpa58904_rewrites(){
    add_rewrite_rule(
        'places/([^/]+)/mypage/([0-9]+)/?$',
        'index.php?venue=$matches[1]&my_page=$matches[2]',
        'top'
    );
}

Then in your template you can access the value of my_page with

get_query_var( 'my_page' );

Be sure to visit your Permalinks Settings page after adding rewrite rules to flush the rewrites cache.