Although you are creating a project under your "default repository location", this does not mean that a Git repository will be created for you. You need to create (or clone) the Git repository before creating a project / solution or using the "Add to Source" option to ensure that a new repo is created for you.
"The default location for the repo is not a Git repository, and the solution folder is not (by default) the Git repository.
The real purpose of VS "default Git repo location" is that the VS-tool system can localize localized locations of localized repositories. It will search for the folder you specify and (I suppose) any subfolders. Any folders that are recognized as the roots of the Git repository will be displayed in the Repositions list on the Connection page in Visual Studio UI.
If you want to use the command line this page on git -scm.com is a small snippet that shows how to create a folder and initialize it as a Git repository (locally). Here is an example showing how to initialize your solutions folder as a new local Git repository from powershell (with msysgit ):
set-alias git "C:\Program Files (x86)\Git\bin\git.exe" cd "C:\_Projects\HelloGitWorld\" git init git add . git status
From there, you can launch a visual studio, download a project / solution, and see that Git integration now works as intended. The same set of commands can be executed from the CMD shell, but you may have to specify the full path to git or just use Git bash (which can be tedious for you if you are not used to using unix shells.)
If you do not want to use the command line tool, you can use Visual Studio Tools for Git and select "New .." from the "Connect to Team Projects" panel (thanks to Edward Thomson for pointing this out) or use a third-party tool like TortoiseGit . This will make it easier to create a Git repository without requiring you to understand how Git works and how to work with the command line. For most scenarios, you can completely rely on Visual Studio Tools for Git. No need for anything else.
I use visualstudio.com and github.com to host projects, as well as the bare (private) repositories on the secure SAN in my house (because, after all, you cannot trust anyone anywhere with your private work. I'm not care what people say.) You can find this article on saintsjd.com useful in resolving the issue of bare repo - this is what you really need, and fooobar.com/questions/30657 / ... to see how to create it by yourself.
Let me know if I can clarify anything or if you need examples.