This is most probably a corrupted Visual Studio installation. Let's just do a Visual Studio repair, or run the installer and make sure you update the "Universal Windows App Development Tools".
Update: (if that does not help)
Well, I looked into this in more detail: so the root cause is most probably that Microsoft removed Application Insights, but during an update the template file for UWP apps was not updated and the Application Insights reference is still there.
To fix it you have to remove it from the vstemplate file. On my machine the location of the file is this (should be similar on your machine…):
C:\Program Files (x86)\Microsoft Visual Studio 14.0\Common7\IDE\ProjectTemplates\CSharp\Windows Root\Windows UAP\1033\BlankApplication\BlankApplication.vstemplate
(Now as you see this vstemplate file is for the "Blank Application" template. If you have this problem with another project template then edit the corresponding vstemplate file)
Then first of all, make a backup copy of the file! Then open it and look for something like this (for the one with Application Insights):
<WizardExtension> <Assembly>Microsoft.VisualStudio.WinRT.TemplateWizards, Version=220.127.116.11, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a</Assembly> <FullClassName>Microsoft.VisualStudio.WinRT.TemplateWizards.ApplicationInsigths..Wizard</FullClassName> </WizardExtension>
And remove it.