I'll answer my own question.
After much trial & error, I've found out how to make the images save to a folder in the root of the site.
If the site is at /public_html/websiteName/ on the server, and you want it to save images in
you need to point it to
in the Upload Director under Global File Upload Settings
WebAssit really needs to document this sort of thing better - after all, we're paying you to save us time in our developing sites.