To clarify your answer for Illustrator. The option is not in the "Save As" dialog box.
The correct answer is
Open you CS6 Illustrator file.
The Save As dialog box opens
Type your file name (DIFFERENT THAN ORIGINAL PLEASE!) and the Save as Type is still going to be Adobe Illustrator (*.AI) **This is where the above instructions threw me, as the Save as type drop down does not list anything about versions to save fo)
Once you click Save, the Illustrator Options dialog box will come up. The first option is titled Version and has a drop down menu. Select the version of illustrator you want to save your file as here, then click ok.
I strongly suggest you give this file a different name than your original CS6 Illustrator version as you may lose some parts of your design in the conversion.