I have two tables on a page that I want to display side by side, and then center them within the page (actually within another div, but this is the simplest I could come up
The problem is that the DIV that should center your tables has no width defined. By default, DIVs are block elements and take up the entire width of their parent - in this case the entire document (propagating through the #outer DIV), so the automatic margin style has no effect.
For this technique to work, you simply have to set the width of the div that has margin:auto to anything but "auto" or "inherit" (either a fixed pixel value or a percentage).