Hi Eric,
Here are the ways that I know of to accomplish this:
Define separate announcements for the various levels of the community such that the announcement at the community level does not cascade down to lower levels.
Remove the Announcements module via Studio from the pages that you don't want it to display on.
Utilize a custom content module rather than the Announcements module and only place it on the pages where you wish to display the announcement.
There may be some other work-arounds, but these are the most commonly-used.
Take care,