How to customize a divs background dynamically using Advanced Custom Fields Plugin?

You can apply a style to the header <div> (or the <header> element), and then add an inline style using wp_add_inline_style().

For example, let’s say you’ve got something like this in your header.php file:

<header id="masthead" class="site-header" role="banner">

(Cribbed from the Twenty Twelve theme.)

Let’s say you’ve set up the neighborhood’s color as post meta-information using update_post_meta() or perhaps a custom metabox of some sort. Now we can pull it out of the meta table and throw it into the inline styles:

add_action(  'wp_enqueue_scripts', 'wpse115373_header_bg' );
function wpse115373_header_bg() {
    global $post;
    // set this to the handle of one of your stylesheets
    $handle="twentytwelve-style";
    // set this to the meta key you've used
    $meta_key = 'neighborhood_color';
    $bg_color = get_post_meta( $post->ID, $meta_key, $single = true );
    $css = "header { background-color: $bg_color; }";
    wp_add_inline_style( $handle, $css ); 
}

Reference

Codex pages for:

• wp_add_inline_style()
• get_post_meta()
• update_post_meta()