I don't really understand why Microsoft tries to hide this from users. I assume that Visual Studio Emulator for Android is something equivalent to Genymotion (which does have some setting to change the Android SDK path).
I'm using Xamarin, have installed it and there is one folder for the AndroidSDK. I have tried renaming the AndroidSDK folder and then running the Visual Studio Emulator for Android and it still run OK. So that means it uses some AndroidSDK located somewhere else.
The serious problem of Xamarin and Visual Studio Emulator for Android using different AndroidSDKs is we cannot deploy the built Android app to run in the targeted Virtual Android device (started by Visual Studio Emulator for Android).
From the VS Emulator troubleshooting (https://msdn.microsoft.com/en-us/library/mt228282.aspx):
• Open Registry Editor by selecting Run from the Start buttons context menu, typing regedit in the dialog box, and choosing OK.
• Navigate to HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Android SDK Tools in the folder tree on the left.
• Modify the Path registry variable to match the path to your Android SDK.
So here you can view/edit your Android SDK path.