Thanks for the replies.
The site is a really straightforward 12-page HTML/CSS job. I built the pages from scratch and in my past experience I've been able to just FTP the files over to the web server and build the directory structure myself. From what I understand Website Tonight is a strictly template-driven interface in that the user chooses one of several prebuilt templates, and what GoDaddy told me is that this is the only way my client's account is able to edit sites.
As I see it my options are to try to get my client to upgrade their account to allow for FTP access (assuming GoDaddy allows this), get them to move to another host, or rebuild the site from scratch again using Website Tonight (I would really like to avoid this).
I guess my question is whether anyone with GoDaddy experience knows if the upgrade option is a viable one, or if once you build a Website Tonight site you are stuck using only that.