Still haven't got anywhere.
Turns out the "all-in-one" installer package for Android Studio isn't exactly all in one. I still have to go through the "SDK Manager" to download a few additional packages - including an actual run-time environment.
The tutorial I am following (which was just written on June 20th - about two weeks ago!) doesn't mention this at all! (http://www.i-programmer.info/programming/android/5887-android-adventures-getting-started-with-android-studio.html?start=2)
http://developer.android.com/sdk/installing/adding-packages.html
I'm downloading packages now - but I'm not sure which packages I should be downloading. I just selected a bunch. Hopefully I'll be able to get a freaking run-time!