I am using the plugin user-avatar I think it is better.
and to make the avatars appear beside the names You can use the function
get_avatar()
In which files ? to display it beside by (name), you need to make a change in the post footer in the file (content-single.php) in the $utility_text values.
===========example:
open content-single.php file of twentyeleven theme and find this text:
%5$s
replace it with:
%7$s %5$s
Then find, this part :
printf(
$utility_text,
$categories_list,
$tag_list,
esc_url( get_permalink() ),
the_title_attribute( 'echo=0' ),
get_the_author(),
esc_url( get_author_posts_url( get_the_author_meta( 'ID' ) ) )
);
replace it with:
printf(
$utility_text,
$categories_list,
$tag_list,
esc_url( get_permalink() ),
the_title_attribute( 'echo=0' ),
get_the_author(),
esc_url( get_author_posts_url( get_the_author_meta( 'ID' ) ) ),
get_avatar( get_the_author_meta( 'user_email' ), apply_filters( 'twentyeleven_author_bio_avatar_size', 20) )
);
Note: this change in the $utility_text values may affect translation of this part of the theme if it isn't in English.