In ATO/Style and Edit Center Column/Content Above the Loop, I entered:
Code:
<?php if (is_front_page() && !is_paged() )
$posts = query_posts($query_string . '&cat=-15,-80'); ?>
This prevents posts from categories 15 and 80 from appearing in the list of front page posts in the center column.
Then I use the Enhanced Recent Posts plugin multiple times as a sidebar widget, to display a certain number of posts from several categories that I do want to show up in the sidebar. Another plugin, Widget Logic, directs which pages these widgets show up on.