For some other job I also had to install Android Studio on my development machine where I have Xamarin in Visual Studio running. Today Android Studio had an update which included Android Studio 2.3. It seems that from this version the standalone tools SDK Manager and AVD Manager are deprecated and this functionality can only be accessed from Android Studio.
Obviously the toolbar buttons in Visual Studio (and I recon Xamarin Studio as well) are no longer working. Was this known to you guys at Xamarin? Is there already an update in the making that has its own SDK and AVD manager in Visual Studio?