Add container to nav_menu sub menu

Use a custom walker, extend the methods start_lvl() and end_lvl.

Sample code, not tested:

class WPSE_78121_Sublevel_Walker extends Walker_Nav_Menu
{
    function start_lvl( &$output, $depth = 0, $args = array() ) {
        $indent = str_repeat("\t", $depth);
        $output .= "\n$indent<div class="sub-menu-wrap"><ul class="sub-menu">\n";
    }
    function end_lvl( &$output, $depth = 0, $args = array() ) {
        $indent = str_repeat("\t", $depth);
        $output .= "$indent</ul></div>\n";
    }
}

Usage in your theme:

wp_nav_menu(
    array (
        'theme_location' => 'your-theme-location-EDIT-THIS',
        'walker'         => new WPSE_78121_Sublevel_Walker
    )
);