Is there an equivalent of "stay" for Ubuntu?
Solution 1:
Compiz Place Windows Plugin may be useful for you but not essentially the same as "Stay" for OSX. Anyway, there are a few other plugins that will allow you to have more control on the position, placement mode and other window features.
From the site:
The Place Windows plugin provides some basic window placement algorithms, to place windows at a natural and sensible place when created.
and
Window Placement Rules
Finally, the place plugin allows you to place matched windows on a certain area of the screen, or a certain viewport every time.
A screenshot is provided here for you to see the "Fixed Window Placement" tab inside of the Place Windows Plugin.
Good luck!