How can I configure Google Play so that it doesn't update applications when I'm using the phone? I'd like to configure Google Play so that it doesn't update applications when I'm using my phone (Samsung Galaxy S3) or tablet (Nexus 7).

Note that I still want to have the auto-update, but only when I'm not using the phone.
You can use an app for automating tasks, like Tasker,  AutomateIt, etc.

Here, for example, is a suggestion for a Tasker profile that enables auto update only when the device is plugged in for charging. You may be able to find an alternative trigger that better suits your needs, like screen off, etc.