Using a single git repository for multiple git projects

You could use git subtree locally to maintain a git repository which is split from your larger repo repository, and push from that split repository. Frankly, though, I'd either use one of the free services that Adam Dymitruk suggests or just pay GitHub a bit more - they do provide an excellent service, after all...

This is going to get very unwieldy very quickly (especially as Git won't let you push pull sub directories like svn will)

I would look at not using Github for storing projects. Tools such as Bitbucket or CodebaseHQ have different pricing models which may well fit you better and give you the simplicity you need.

Alternatively, look at something like Gitosis, which can be made to be very Github-esque via tools like Gitlab