Final Code

// Tells WP to add a Menu section
add_action( 'init', 'create_my_post_types' );

// WP Menu section attributes
function create_my_post_types() {
    register_post_type( 'menu',
        array(
            'labels' => array(
                'name' => __( 'Menus' ),
                'singular_name' => __( 'Menu' ),
            ),
            'public' => true,
            'menu_position' => 5,
            'taxonomies' => array('category'),
            'supports' => array('title','editor','excerpt','thumbnail'),
        )
    );
}

// Tells WP to add a new meta box
function create_my_meta_box() {
    add_meta_box("price-meta", "Item Price", "price", "menu", "side", "low");
}

// Echoes the content of our meta box
function price(){
     global $post;
     $meta = get_post_meta($post->ID, 'price', true);
     echo '$ <input type="text" name="price" value="'.$meta.'" />';
}

// Saves the content of our meta box
add_action( 'save_post', 'save_meta_details' );

// WP meta box attributes
function save_meta_details( $post_id ) {
    global $post;
    // Skip auto save
    if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) {
        return $post_id;
    }
    // Check for your post type
    if( $post->post_type == 'menu' ) {
        if( isset($_POST['price']) ) { update_post_meta( $post->ID, 'price', $_POST['price'] );}

    }
}

// WP Hook to execute meta box action
if (is_admin())
    add_action('admin_menu', 'create_my_meta_box');