Pull GetOption() variable into jQuery dynamically created html

Two possible solutions here-

Solution one is to not hardcode the modal markup into the template and instead use the wp_footer action to insert it, along with your data:

function wpa_wp_footer(){
    $someval = 'foo'; // get_option results
    echo '<div id="modalpopup"><div id="inside">' . $someval . '</div></div>';
}
add_action( 'wp_footer', 'wpa_wp_footer' );

Personally, I would do it this way, as simple as it gets, keeps it theme-agnostic.

Solution two is more in line with your original idea, and gets the data to javascript so you can insert it yourself. But instead of making a separate request for the data via ajax, localize the script to have the data printed to the page when it's rendered.

Here's your standard enqueue for adding javascript to a theme, along with the localize call to add extra data.

function wpa_scripts() {
    wp_enqueue_script(
        'wpa_script', // script handle
        get_template_directory_uri() . '/js/script.js',
        array('jquery'),
        null,
        true
    );
    // do your get_option here to set whatever data you're passing
    $script_data = array(
        'some_var' => 'someval'
    );
    wp_localize_script(
        'wpa_script', // the script handle enqueued above
        'wpa_data',
        $script_data
    );
}
add_action( 'wp_enqueue_scripts', 'wpa_scripts' );

Then in your javascript, access the data like:

jQuery('#inside').html( wpa_data.some_var );