Ha! So, it looks like I can link to images if I change the file extension from ".jpg" to ".htm". This fools topcities into thinking its serving up a webpage. But, the HTML in the post tells your browser it's really an image.
My first attempt was with a ".txt"... but, it seems topcities doesn't appreciate links to text files either.
This would probably work with most freebie-non-image-sharing webhosters.
It's not a new trick.. I was just trying to remember how it's done.