I need to move Git to a new location and was wondering if there's a way to just rsync my git repository to a new location?
rsync, or just clone, as git clones are complete copies of (the reachable parts of) the source repository.
You can use
git remote add servername master git push servername master
Replace servername by you new git repository
I am no git expert, but where do you see the problem in doing exactly that? Of course, you will need to inform the users about this change and if it's not your machine, talk to the admin to set up the server part, but other than that, git repos are just directories with some (or a lot) files.
scp -r will do the trick just fine.