How about some maps?

Most folks are unaware where the Byzantine Empire was located. It is easy to remember the location if you think of it as the Eastern Roman Empire. If you are not aware of where the Roman Empire was, then, well, read an history book.

Here are a few images for the geographically-challenged.

Here is the empire just about at the nadir of its fortunes - ca. 1355.

Here is an image illustrating military provinces in the mid-empire.

Lastly, this map shows the Western and Eastern Roman Empires before the West "fell."