Installing MonoGame (at least in current version 3.2) for Visual Studio 2013 can result in the templates not being available for new projects.
This is quite often the result of the Windows user management not being considered in the MonoGame installer: Visual Studio is run under a different account (usually a user account) than MonoGame was installed from (usually an admin account). The templates should be in the "documents\Visual Studio 2013\Templates\ProjectTemplates\Visual C#" folder, but are instead installed into the admin templates folder.
Should that be the case, simply copy the MonoGame folder from
C:\Users\<admin>\Documents\Visual Studio 2013\Templates\ProjectTemplates\Visual C#
to
C:\Users\<user>\Documents\Visual Studio 2013\Templates\ProjectTemplates\Visual C#
That should fix the problem.
