I'd love to be able to go out in my backyard and to dig up some graphite, but alas, that will likely be fruitless.
It isn't that I need to find a large cache, but just enough to supply one pencil. I've learned that graphite can be found in the veins of metamorphic rocks. Particularly limestone deposits. I'm aware of some limestone here in Utah, in fact a contractor for applications of this type of rock are headquartered in my town of North Salt Lake.
Here's some free advertising for Hughes General Contractors, Inc.