Allow admin login at /admin

another option – redirect /admin/ to wp-login.php with a parse_query action hook:

function wpa53048_parse_query( $query ){
    if( $query->query_vars['pagename'] == 'admin' ):
        wp_redirect( wp_login_url() );
        exit;
    endif;
}
add_action( 'parse_query', 'wpa53048_parse_query' );

EDIT

Well the above apparently only works with certain permalink structures. Here’s another method hooked to parse_request:

function wpa53048_parse_request( $query ){
    if( $query->request == 'admin' ):
        wp_redirect( wp_login_url() );
        exit;
    endif;
}
add_action( 'parse_request', 'wpa53048_parse_request' );