This seems easy enough… i just need a query to check for all the categories with a parent of the current category… but how do you write custom queries?
Are you trying to show children or just find out if there are any there?
To find out if any are there, check your ADMIN > MANAGE > CATEGORIES (I know that sounds too simple, but sometimes people just don’t know these things – making no assumptions about you.)
To show the categories with the children (ONLY if there are posts in the category will they show), check out:
http://codex.ww.wp.xz.cn/Template_Tags/wp_list_cats
http://codex.ww.wp.xz.cn/Template_Tags/list_cats
If you are looking for a specific “If categories” conditional tag:
http://codex.ww.wp.xz.cn/Conditional_Tags