If you want a place to store or archive personal projects (because you don't want to pay for private Git hosting?) features like wikis and issues become rather irrelevant, and if you want to move that data to or from GitHub, that takes some effort to be explicitly exported instead of just adding a new remote.
If you're trying to keep your own code, running your own Git server is simple if you have SSH (or not even SSH if you want to create a local "server"). The Git website has a simple tutorial for this: http://git-scm.com/book/en/Git-on-the-Server-Setting-Up-the-...
I've also simplified this workflow into a tiny command, "mygit": https://github.com/interestinglythere/mygit
As for running a GitHub clone, unless you have some really edge-case needs or you really don't want to pay for private collaborative repos, your time is probably better spent maintaining your actual code. In addition, having your code on a social site will make it more receptive to contributors. If you don't want contributors, why do you need a /Git/ server? (If it's because that's how you like to manage your code, see my first point.)