So, within a webapp.RequestHandler subclass I would use self.request.uri to get the request URI. But, I can't access this outside of a RequestHandler and so no go. Any ideas?
I'm running Python and I'm new at it as well as GAE.
You should generally be doing everything within some sort of RequestHandler or the equivalent in your non-WebApp framework.  However, if you really insist on being stuck in the early 1990s and writing plain CGI scripts, the environment variables SERVER_NAME and PATH_INFO may be what you want; see a CGI reference for more info.
Get the request uri outside of a RequestHandler in Google App Engine (Python)