You are correct that there is no "template" for Visual Studio 2010 C# projects.
Templates can be created by you, however.
What you need to do if you want to start a project with C# is the following:
Project -> New Project/Workspace -> Create New Project
(Don't Create project using templates!)
In the dialog that pops up, select the Settings tab. Make sure the checkbox "Compilable is checked. Then click the button, "Set/Change Compiler". Scroll down the list of compilers to Visual Studio 2010 and click on it. Now you will see selections for Visual Basic Compiler, Visual C# compiler, Visual C++ Compiler, and Visual J# Compiler. Click on the Visual C# compiler option here. Now you can select from Class Library, Console Application, or Windows Application.
If needed, you can edit the configuration and make that new configuration local for only that project or global for all new projects as well. In most cases, you shouldn't have to edit this particular configuration.
The difference between creating a new project from scratch like this and using a template is that a template will give you a "starter file" that will help you get started coding. This generally isn't necessary for me, but creating a new template isn't that hard.
I'm a bit busy today, and will be out of town for a couple of days. However, sometime during the first part of the week, possibly by Tuesday or Wednesday, I would be happy to see if I can create templates for C# that can be shared with other users.