In my home directories, I usually store source code (whether as a decompressed tar ball or a Git/Subversion working copy) beneath $HOME/src slightly inspired by the FHS. I want to keep bare Git repositories separate from those.
Is there any convention where to store bare Git repositories in home directories?
When I don't have control over a system and can only access it as a user, I have tried in some cases to treat my home directory a little like it's another FHS / or /usr directory.
So I have /home/me/var/git/whatever.git (bare repository) and /home/me/src/whatever (working repository), along with /home/me/bin, /home/me/lib, and /home/me/share/, etc for single-user locally installed software.
This has worked okay for me, but it does require for consistency that you are careful about organizing what goes where, and not letting random programs writing garbage whereever they want.