When I create a new web project with Visual Studio, I only see the templates in the picture below:
The MVC one is missing and so I can only create empty projects.>
I had the same issue with the MVC template not appearing in VS2015.
I checked Web Developer Tools when originally installing. It was still checked when trying to Modify the install. I tried unchecking and updating the install but next time I went back to Modify, it was still checked. And still no MVC template.
I got it working by uninstalling: Microsoft ASP.NET Web Frameworks and Tools 2015 via the Programs and Features windows and re-installing. Here's the link for those who don't have it.