I don't know where the config files are stored for .NET Add-ins, other than referencing the link I provided. With Java add-ins, you can rename the add-in file to .zip and see how it is bundled together.
[ATTACH=CONFIG]16794[/ATTACH]
So if I were going to create a properties file or xml file to store application settings, I would choose a location such as the user's home directory, or some other directory for this specific add-in. While it would be nice to use the classpath of this add-in, making the change for me would require the end user needing to rename the add-in to .zip, extract it, change the settings, rezip it, rename it to .esriaddin
One mistake and you're stuck (as the end user).