Add classname comment template from functions.php

You should consider hooking into the comment_class() and post_class() filters, if your theme supports it.

Using the comment_class filter:

We can add the following filter:

/**
 * Add a custom comment class, based on a given comment author's user meta field.
 *
 * @see http://wordpress.stackexchange.com/a/170443/26350
 */

add_filter( 'comment_class', function( $classes, $class, $comment_id, $post_id ) {

    // Custom user meta key:
    $key = 'city';           // <-- Edit this to your needs!

    // Fetch the comment object:
    $comment = get_comment( $comment_id );

    // Check if the comment author is a registered user:
    if ( ! is_null( $comment ) && $comment->user_id > 0 )
    {
        // Check for the custom user meta:
        if( '' !== ( $value = get_user_meta( $comment->user_id, $key, true ) ) )
            $classes[] = sanitize_html_class( $value );
    }

    return $classes;
}, 10, 4 );

Output example:

<li class="comment byuser comment-author-someuser bypostauthor 
           odd alt depth-2 reykjavik" id="li-comment-78">
    <article id="comment-78" class="comment">

where the reykjavik has been added as the city user-meta, for the given comment author.

Using the post_class filter:

Similarly for the post_class filter, we can use:

/**
 * Add a custom post class, based on a given post author's user meta field.
 *
 * @see http://wordpress.stackexchange.com/a/170443/26350
 */

add_filter( 'post_class', function( $classes, $class, $post_id ) {

    // Custom user meta key:
    $key = 'city';           // <-- Edit this to your needs!

    // Fetch the comment object:
    $post = get_post( $post_id );

    if( ! is_null( $post ) && $post->post_author > 0 )
    {
        // Check for the custom user meta:
        if( '' !== ( $value = get_user_meta( $post->post_author, $key, true ) ) )
            $classes[] = sanitize_html_class( $value );

    }

    return $classes;
}, 10, 3 );

Here’s a shorter version that works within the loop:

/**
 * Add a custom post class, based on a given post author's user meta field.
 *
 * @see http://wordpress.stackexchange.com/a/170443/26350
 */

add_filter( 'post_class', function( $classes, $class, $post_id ) {

    // Custom user meta key:
    $key = 'city';           // <-- Edit this to your needs!

    // Check for the custom user meta:
    if( '' !== ( $value = get_the_author_meta( $key ) ) )
        $classes[] = sanitize_html_class( $value );

    return $classes;
});

Output example:

<article id="post-1" 
         class="post-1 post type-post status-publish format-standard 
                hentry category-uncategorized reykjavik">

where the reykjavik has been added as the last post class, based on our filter above.