Visual Studio 2012 does not have SharePoint 2013 template
Funny thing occurred when i try to open Visual Studio 2012 and there is no Project Template for SharePoint 2013.
If you are having the same problem. Probably you need to install the following item
Microsoft Web Platform Installer 4.5
Once installed, open this Web Platform Installer and look for One of the key components is the Visual Studio
Microsoft Office Developer Tools for Visual Studio 2012
You should be able find it under “Products” >”Tool” category.
Download it !