The "hang" occurs then you try opening the Xamarin in the Options window. Visual Studio will stop working here so you can't set the paths for Xamarin.
So I went digging through the Xamarin logs in the AppData folder. I know where the log folder is from a previous issue with Xamarin. Xamarin is a good idea but it's buggy as fuck. So navigate to %USERPROFILE%\AppData\Local\Xamarin\Logs\15.0\ folder and see which is the latest log and open it with your favorite text editor.
Once we confirm, if it's really the missing SDK and NDK paths, we then have to add them to Window's Registry.
- Open regedit
- Navigate to Computer\HKEY_CURRENT_USER\SOFTWARE\Xamarin\VisualStudio\15.0\Android
- Right-click and add new String Values
- AndroidNdkDirectory - set it to the full path to where you install the NDK
- AndroidSdkDirectory - set it to the full path to where you install the SDK
And we should have fixed the issue.