Since it has to be a writeable directory, it would have to be something like the /includes, /stylesheets, images/graemlins, or images/icons folders because you proabably can't change permissions any more w/o ftp or telnet. As long as you correctly set permissions at installation and haven't changed them, there should be several writeable directories in your ubbthreads tree.
EDIT:
If you have a directory for attatchments, that should also be writeable already as well
